Tires, if you think they have life on them yet, then keep them. A three week tour won't put that much wear on them.

Brakes need to be checked, that is the one thing that if it fails, you learn about it at the wrong time and have a really bad day. I have never run disc brakes, get advice from someone else on what to look for.

Racks and bolts, I suggest putting blue locktite on all rack bolts and if you have a kickstand, those bolts also. A good hardware store like Ace or True Value should stock replacement bolts along with the blue locktite. Yes, they have different depths. I carry a couple spare bolts.

It is very common to forget to check bolts in shoe cleats if you are using cleats, but that is something that you should do. When you first install a cleat, you are compressing some plastic in the sole, that plastic deforms a bit over the next few weeks and the bolts get loose. If you do not retighten them, a bolt can fall out and then you can't release your shoe from the pedal. Over time teh plastic stops deforming and they stay tighter but I check these bolts for tightness every couple of months and carry one spare cleat bolt.

A visual inspection of just about everything else should be adequate. And, if something feels wrong on the bike, try to figure out what that is. It might be something serious or it might just be the way you packed your tent, in which case it is not a problem.