How "bad" is a Taiwanese accent on the mainland? If I learn to talk like my co-worker from Taipei, is that likely to make things difficult for me on the mainland (whether by impeding understanding or by arousing suspicions)?

I have no idea if and when I'll visit either China, but I've been considering it.
It is not "bad" at all.

People speak mandarin in Mainland China and Taiwan can understand each other without difficulty.

There are some word usages differences though, but usually it is not a problem.