This is all a bit of a superficial take on it. Yes, even Arab Christians use the word "allah" for God, but there is a major difference in its usage. Muslims identify this as a personal name for God, whereas the Christians are using it as more of a title. It gets confusing.
Allah is one of 99 names attributed to God by Muslims. These names range greatly but some include:
1 Allah (الله

(The) God
2 Ar-Rahman (الرحمن

The All Beneficent
3 Ar-Rahim (الرحيم

The Most Merciful
4 Al-Malik (الملك

The King, The Sovereign
10 Al-Jabbar (الجبار

The Powerful, The Irresistible
11 Al-Mutakabbir (المتكبر

The Tremendous
12 Al-Khaliq (الخالق

The Creator
13 Al-Bari' (البارئ

The Maker
29 Al-Hakam (الحكم

The Judge, The Arbitrator
30 Al-`Adl (العدل

The Utterly Just
31 Al-Lateef (اللطيف

The Subtly Kind
32 Al-Khabeer (الخبير

The All Aware
61 Al-Muhyee (المحيى

The Giver of Life
62 Al-Mumeet (المميت

The Bringer of Death, The Destroyer
73 Al-Awwal (الأول

The First
74 Al-Akhir (الأخر

The Last
75 Az-Zahir (الظاهر

The Manifest, The All Victorious
76 Al-Batin (الباطن

The Hidden, The All Encompassing
98 Ar-Rasheed (الرشيد

The Guide, Infallible Teacher and Knower
99 As-Saboor (الصبور

The Patient, The Timeless
... and so on. Most Muslims simply refer to Him as Allah, but there are also examples of various names for Him in the Hebrew scriptures. Even Christianity has several names for God, including "Lord", "The Father" and so on.
To address the first statement, calling Allah Jehovah/Yahewh does not make it so. Just because Muslims say that Allah is the same as the others does not mean we are compelled to accept this answer. (I suppose we can turn that argument around, too.)
Muslims don't believe that their religion started with Muhammad (pbuh), instead, they believe that it ended with him. Adam (the first man), Moses, Jesus, etc. are all considered prophets of Islam (pbut), because they communicated or received revelation from God. That means until the time of Jesus (pbuh), Judaism and Islam overlapped. Following that, the Jews that didn't believe in Jesus as a prophet, and the Christians that believed in him as synonymous with God diverged from Islam. When Muhammad (pbuh) shared his revelation, he began to restore the belief of the Oneness and Unity of God.
Beyond the name, there are important differences in God's nature among the three, but particularly between the Judeo-Christian tradition and Islam. To say that there are only differences of prophets makes it sound more like the ancient syncretic polytheists; the Greeks and the Romans identifying their gods of war comes to mind.
I'd say there are far more similarities between the Jewish and Islamic conceptions of God than the Trinitarian Christian conception. Judaism and Islam both stress God's complete unity and reject associating any partners with Him. They also depict a more vengeful God, rather than one that does absolutely no harm. For instance, the plagues of the Old Testament take the lives of the oppressing and polytheistic Egyptians, especially the plague that claimed their firstborns. When Pharaoh's army chased the Hebrews into the sea, they weren't just prevented from reaching the Hebrews, they were drowned. There are many examples of this.
On the other hand, God as described by many Trinitarian Christians and equated with Jesus himself, is portrayed as pacifist.
I'm very interested in hearing why you think that the Jewish and Christian concepts of God are more similar than the Jewish and Islamic concepts.
The Koran portrays the Christians as polytheists because they worship the Trinity. "They do blaspheme who say: Allah is the third of three." There is evidently some sort of difference to them.
However, let me quote here from another site I found about this issue:
"Muslims believe that Allah of the Quran is the same as God the Father of the Holy Bible since they do not believe in God the Son, Jesus Christ, nor in God the Holy Spirit..."
So they do want to identify Allah as God the Father, yet they regard Christian beliefs as heretical. The real point of contention, I suppose, comes in the nature of the Trinity and the person of Christ. But beyond this there are fundamental differences in the character and nature of Allah and Yahweh, which are far too complicated to address here.
Muslims believe that Allah is the same God worshiped by Jews and Christians. Although they believe that Trinitarian Christians are misled (and blaspheming) by equating Jesus Christ with God, they don't accuse them of worshiping a different God.
Remember, Jews and Christians are recognized as people of the book in Islam, and it is forbidden to prevent them from practicing their religion.
Now, I believe you can successfully argue that the Jewish God and Christian God are, historically, the same. The difference here is that their natures (aside from trinitarian issues, though that's a very important distinction) are quite similar, and you cannot necessarily say the same thing for Allah and Yahweh. We also get into alternative histories, different kinds of involvement in human affairs, etc.
If you do believe there are strong arguments regarding the differences in character of "Allah and Yahweh" (as described in Judaism), compared to the Trinitarian conception of God and the Jewish conception, I'd be happy to hear them

.
My point is that it is too simplistic to say that all are worshipping the same God. If you are going to identify "God" simply as the ruler/creator of the universe, then yes, we can say that they are all the same -- and probably half of the other religions of the world, too. (My, aren't we all just one big happy family...) But if you're going to lay out details about God's character, his personal attributes, role in the world, commandments, etc., then we start to run into problems.
Again... I'm eager to hear your arguments!
Trinitarian Christians may believe that Allah is not the same God they worship, but that doesn't make the reverse true.
What's interesting is that is the same type of comment we hear from Muslims regarding their radicals. They're not real Muslims but in the meantime Sunnis and Shias are killing each other in the name of Allah.
I'm really tired of hearing this misguided line of thinking expressed as fact. Sunnis and Shi'ites are only presently fighting on any significant scale and for "so-called" religious reasons in Iraq. This has more to do with the failure of the US occupation, the ineffective Iraqi government and the actions of small minority of disgusting people. The problem has been made worse because the government and Coalition forces have been unable to provide security for the people. The result is steadily mounting sectarianism, not because Sunnis think Shi'ites are "non-Muslims", blasphemers, or worse (or vice versa), but because people are concerned about their safety from the horrible minority that actually goes out and commits sectarian killings and crimes (like Al-Qaeda or certain Shi'a groups), they feel much more secure taking refuge with what's familiar and safe. Often that might be their religious community or their tribe (which is almost exclusively of a single sect).
The problem here is that when one family loses a father, mother, brother, sister, daughter, son, or any other member, some people are so overcome with grief and so distraught about the lack of justice in the chaotic society that they try to seek justice or get retribution themselves. Sometimes this only serves to further escalate the situation.
We're talking about a country with millions of refugees, millions of people internally displaced, hundreds of thousands of widows caring for (as many as 7 or more) children by themselves and so on. There are at least 300,000 widows in Baghdad alone.
What people should realize, if they want a more accurate understanding of Sunni-Shi'a relations, particularly in Arabic countries is that there is a large amount of intermarriage between these faith communities. This occurs wherever the groups mix, particularly in Iraq, Lebanon and Yemen. There is a simple solution to the question of what the children will be, they follow their father.
Lebanon is also a textbook example of intermarriage between Sunnis, Shi'as, Catholics, Orthodox Christians and Druze. I recently watched a wedding video of a Shi'a relative of mine marrying a Sunni woman he met at University. This is not something uncommon in Arabic countries.
Also, I think the majority of Mosques, especially those in the West, would never forbid a member of the other sect from praying within, or in congregation. Most Muslims agree that both Sunnis and Shi'as are Muslims and furthermore they realize that the origin of the difference is more political than theological.
Maybe they're in the process of having a reformation too and the Bahais are the only real Muslims.
I'm curious about this statement. Are you yourself Baha'i?