You can buy window film kits at home depot for leas than $10 that stick on with double sided tape (which easily pulls off). That lets you put a plastic water barrier on a few sides to protect from mist overspray, but it is a fine, focused mist so its not like a spray bottle spraying outside your cage.
Holes can be smaller by putting the zip tie right up against the frame but its too late for that. You might want to support your plants with some vertical branches which will help keep the holes from getting bigger. Plants will hide the holes. You can also find these cages on Craigslist for around $50 usually... so while you dont want to just throw away money, if he is really that upset you can probably find a replacement.