Know what's worse? Check the soldermask layer... in extreme cases you can end up with soldermask openings overlapping the adjacent copper, exposing it!
Easy solution: don't use stupid square pads, they're ugly, their corners don't work right, and probably something about stress or solderability or something, I don't know. I prefer them for aesthetics if nothing else, but Altium's functionality on square corners is obviously an issue...
If you don't want to go through your libraries, this can be done on the PCB: open PCB Filter, query
IsPad AND (PadShape_AllLayers = 'Rectangular')
go to Properties (older AD: PCB Inspector), change pad shape to Rounded Rectangle, set Pad Corner Radius to say 5-30% (depending on if you want it to look basically square still, but be handled as rounded to get the right corners, or to round it off visibly).
May have to insert additional steps if you have pad stacks in the design, obviously.
BTW, you can do this in the libraries as well, just query and edit the whole library; do set aside some time to inspect everything and make sure it didn't bone anything up, though. The warning that you "can't undo" the operation is worth heeding.

Tim