Best to play ME first as the stories are linked.
As for the bugs, the answer is a resounding YES, ME2 is still incredibly buggy, I played it in the summer running latest patch and for a AAA title it is probably the buggiest I've found in a very long time with the exception of Fallout: New Vegas. I can understand how loophole / quest bugs happen but ME2 has some unforgivable flaws in it's basic game mechanics.
Probably the worst bug is some sort of clipping issue that can see you getting stuck in the scenery forcing you to reload a previous save, absolutley shocking I struggled to play for more than about 20mins without it happening, it would even happen on your ship sometimes! Thankfully you can use an editor to bind a key to noclip mode and use that to escape.