The stupidest thing I see civs do, over and over, is make weak attacks, with too few of their total forces, and give up those attacks too quickly when they could have carried through and wiped me out. When a human player organizes an invasion of their opponent, you send your best and strongest and mostest, as many as you expect it will take to accomplish the mission. I'm sure most players overstock their invading forces as much as possible, as opposed to skimping on them. It's because we know stuff happens, and you don't send a pack of girlscouts to do the work of ten armored divisions.
But a huge majority of the time, I see civs at all stages of the game sending small fractions of their total forces, and often not even the best units they have on hand. When I'm curious about such things, I just push the mod button on my interface that removes fog of war, and you can see all of the enemy units they have squirreled away everywhere in the world. Many a time, I've seen huge military powers with militaries many times my size, send out just a handful of units to attack me, while leaving 9/10th's of their more powerful forces idling around doing nothing. Another of their favorite tactics, is to send out sporadic piecemeal waves of forces... each one too small to succeed, each one easily defeated, and never all of those forces together in one powerful element.
And many a time, even if they do happen to send a powerful force that could settle my hash, if I bloody their nose good on the first rush, their attack will usually fragment and hie off in all directions like startled cockroaches, instead of sticking together and pressing a solid attack and using reserves to finish off my lesser number of badly wounded remaining units. Then you kill the scared cockroaches easily, and the rest take off for home with tails between legs.
I used to feel like Custer when I saw a big force coming towards my little, budding cities... "OMG, this is it! Game over, man, game over!" Now, I've played long enough to just think, "Ok, what stupid tactic full of fail are they going to use, this time?"