Not so much "irregularities" as things they didn't expect or things they didn't understand. Like curing mail ballots by getting voter addresses and writing them on the envelope, which was authorized by state law and had been going on for several years.

One particularly funny objection was that districts run by Republicans decided not to cure mail ballots, even though that was explicitly allowed by state law. I guess they thought that would disenfranchise more Democrats than Republicans. Anyway, Giuliani et al claimed that was unconstitutional because voters did not get an equal chance of having their vote count. But this was an act by Republicans to not count Democrat's ballots!