fluffy
The only impression I got from this video, and not knowing much about Bloomberg's track record, is that some random dude has decided to take up the cause of being against term limit changes, and keeps bringing it up in press conferences which have nothing to do with it.

I'm not really sure what the problem with extending term limits is supposed to be, anyway, at least for nonpartisan positions such as mayor. If the people are tired of a candidate then they'll vote for the other (presumably better) candidate.

fatatty
I would say the mayor of NYC is probably a fairly partisan position. I know a lot of Democrats hated Giuliani despite being a fairly left leaning candidate. Bloomberg himself was a lifelong Democrat, but ran as a Republican, probably to take advantage of Giuliani's post 9-11 popularity, who ended up endorsing him.

Say what you will about term limits but they are there for a reason and any time they are encroached on it's hard to not see them as a power grab, and a potentially slippery slope. They're there to limit power, and a NYC mayor without term limits could be a very dangerous thing regardless of party. Bloomberg may not be corrupt and is obviously a decent mayor, but extending term limits gives that new power to every new mayor for the city from here on out.

That said, I'm sure he's answered this question 100 times already and was probably just sick of it.