Will changing the server date/time cause problems?

A client of ours has requested that we change the time on the server to
match their time zone (one hour ahead of us). Are there any know issues
or gotchas to look out for when bumping the server time forward an hour?
I couldn't imagine any issues occurring, since it's really just like the
server when 1 hour without performing any activity. Obviously any fields
in the database stored with a time without a timezone would be off
afterwards, but that's not a huge concern.

Another client has requested the same thing, but their time is two hours
behind us. This is the change that I'm more worried about, since you are
going to have some data/time overlap on the server after the change is
made. Are there any known issues with this situation in Postgres? Should
everything be shutdown prior to the change, then restarted again?

Thanks.

Justin Pasher