For the time that the cigars are in there for the wedding, it really won't matter if it leaks a bit.
Now, such being said, if you want to seal the humidor anyway, probably wouldn't hurt to figure out where the leaks are. Are they around the glass where it is set in the wood or just around the door? Or at the hygrometer cutout?
The door is easy, and the likely culprit. Just check the gap - you can slide a dollar bill around with the door closed to check, if it sides easily, it's probably not sealing well. Adjust the hinges if necessary pr go to a better vinyl weather stripping. Also check the door for warping and not being mounted evenly. An uneven mount you might be able to adjust the hinges, but if it's warped, you're probably out of luck.
As for the glass, you can pop the wooden pieces out that hold the glass in place (drawing a total blank on what they are called), take the glass out, put down a bead of silicone sealant, reinstall the glass and then reinstall the wooden pieces. Or you could just run a bead around the gap without disassembly, but it will be visible. If they don't leak, I wouldn't mess with them, too much potential for damage or broken glass.
For the hygrometer, just pop it out and put some silicone sealant in the hole & around the lip, then reinstall it. Wipe up the excess sealant and it should be taken care of. Although a significant leak here is unlikely.
