I have noticed that sometimes the knots (not the strings) on a the tzitzit from a Tallit Katan or a Tallit Gadol either come or become tangled. Is it permissible to untie and then retie the tzitzit? I don't see a reason why it wouldn't be, but I wanted to ask.
As far as I know(I am not a Rav): there is no problem, Moreover - if the first knot (that is near the talit) became loose the Tzizit might not be Kosher. If you re-tie the first knot you should cocentrate "L'eshem Mitzvat Tzizit" since it is the "Mederoita"
I don't think there should be any problem at all, but maybe you should remove the tallis or tallis katan while the tzitzis are untied, because having a length of 12 gudalim tied is required miD'rabbanan.
If you untie the second knot (i.e. the second of five double knots, starting from the hole) you definitely would have to remove the garment, because without a knot, some windings and a second knot you don't even have tzitzit min HaTorah, so you would be מבטל מצוות עשה if you are wearing it at that point.
If I'm not mistaken, the Gra holds that you can't say a bracha on tzitzis if they are tangled, so you would have to take care of the problem before putting on the tallis or tallis katan.