Thanks for stopping by Stas. Would be nice to have you posting around here again... miss your lovely thoughts. 
Personally, I would consider adding an amendment to increase the number of years a President can serve (maybe to 12-15 years if the guy deserves it). Also, replace electoral college with popular vote, legalize gay marriage, and something to balance budgets or get rid of the white collar cheaters.
I'd agree with the allowing a president to serve more than 2 terms. It used to be traditional not to run more than 2 terms, but FDR did it and won. After that, they decided they must do that to prevent the USA from becoming like a Monarchy.
I hate the electoral college, but there are some good reasons for it. Super small states don't have much say in the popular vote, so candidates may ignore them. With the electoral college, you cannot completely ignore them, because you might need 4-5pts. I would be in favor of splitting up the electoral points within the states to districts or something. This way states like Texas and Georgia which we live in aren't a lost cause for a non-Republican vote. Also, in states like NY and CA, rural areas that would vote non-Democratic could be heard as well. It would make it more complicated, but it's a good compromise from the popular vote and the electoral vote.
Gay marriage, I really don't care what gays do. I'm not gay, so it doesn't effect me one way or another. Go ahead and legalize it.
You would have to go into more details about your last one for me to really know what you are talking about. There are many things that could be done and many ways people cheat. Also, is that really amendment worthy?