@noto2: yes, you have a point. But note that tank has a railway, while chariot has only slow road in the best case to travel on. So the difference is actually in roads. It would be interesting to implement such thing as sea routes, which would be faster to travel on (not on enemy territory though). Then there would be similar 'commando' promotion for naval units (difficult to get to of course). But unfortunately this is probably really difficult to implement in Civ4 
Simply leveling naval units' speed would mean the same speed in ancient and modern eras. And it's not realistic too.
One amendment that can be easily done (this isn't the real solution, but still interesting): pillaging is allowed only for ships with full movement, so that they have to stop at a resource tile in one turn and pillage it in the next one. This can be combined with the same fix for bombardment and removing transported units' movement points (as I described in my first post here).
After these fixes only
1) unexpected attack of naval unit outside of city
and
2) fast movement itself
would remain valid out of the fast movement problem, which you described.

Simply leveling naval units' speed would mean the same speed in ancient and modern eras. And it's not realistic too.
One amendment that can be easily done (this isn't the real solution, but still interesting): pillaging is allowed only for ships with full movement, so that they have to stop at a resource tile in one turn and pillage it in the next one. This can be combined with the same fix for bombardment and removing transported units' movement points (as I described in my first post here).
After these fixes only
1) unexpected attack of naval unit outside of city
and
2) fast movement itself
would remain valid out of the fast movement problem, which you described.