Is there any problem with taking a nap with tzittzit on? I know the Gemara says that in those days Tefilin would be removed (which I can understand), but would we also treat tzit-tzit that way?
There is no problem of napping with tzitzis. The holiness of tefillin requires a guf naki, a clean body, and it is forbidden to nap with tefillin on because of the concern of flatulence etc. This does not apply to tzitzis, and poskim explain that it is better to keep tzitzis on while sleeping, both to continue to fulfill the mitzvah, and to avoid concerns of making the blessing again when putting the tzitzis back on.