Tears in clothing, and external mesh ripped on pack and seams coming open and/or tears in pack fabric --- fixed all of these with a sewing needle and dental floss as 'thread'.

Duct tape fixes cuben fabric well; less so other stuff, though I've also fixed a pack fabric seam split this way (not at a weight-bearing spot ...). For actual stuff that happens, duct tape is useful but I think a bit over-hyped. You know the old chestnuts, such as "just need duct tape and WD-40: if it moves and it shouldn't duct tape it, if it should move and doesn't, use WD-40". Dental floss and a needle has proven more useful to me than duct tape.

Shoe fabric uppers wearing out, big holes. Solution? Nothing, I've not found a good on-trail solution apart from just living with it until the shoes can be replaced.

Trekking pole broken: find a useful stick until can replace. Titanium trekking pole bent: bend it back!

Gaiter cord that goes under shoe wears through and breaks: stop using such cords. In fact, I kept one cord on, but stopped putting it under my shoe; it made it quick and easy to tell the left gaiter from the right one.

Gatorade or pop bottle type of water bottle gets mold in it: buy a new drink at the store.

Windshirt got a hole in it; temporary repair with duct tape, longer term repair at home using seam sealer.

Aluminum caldera cone bends out of shape and won't stay closed; paper clips. Then later took some time to re-bend the tongue-and-groove.

The usual patch kit for inflatable mattresses. I find that I can get by with about half of the repair kit that comes standard. In-the-field identification of the leak can be relatively easy or hard, and in fact, sometimes with all the time in the world at home it can be hard to find a slow leak. Patching usually works, though I've had one case (an inflatable pillow) where it just never worked well enough.

Tent leak at ridegeline --- I had one of these too, right at a spot where some elastic was sewn in, only showed up under pretty hard and sustained rain. I found that once the tent was even a little wet on the outside (and I could wet it myself in advance if desired), I could 'stick' a black yardwaste bag outside the tent to cover the spot. Might not have worked in high winds, but it served me a few times.

I find that, even with relatively lightweight gear, stuff really lasts quite well if reasonable care is taken. I.e., I find that clothing/equipment 'failure' is very very rare, and generally a little common sense and flexibility will suffice to deal with it.