I like Bashir but I think he was the weakest of the credits characters.
It was never his arrogance that bugged me about him. I think the massive genetic retcon did more harm to his character than good, especially since it didn't make much sense given his behavior the first few seasons.
What bugged me about him at the start was his obnoxiousness. Always butting in on things talking his head off, defined mostly by his lustfulness. As Worf put it, 'He is an overgrown child', and they didn't figure out how to make that endearing for a couple seasons.