What should I check after my kitchen cabinets are resurfaced?
In terms of the look, if it looks good to you, it is good. In a more empirical sense, in our finishing room we look for consistency/homogeneity of color, evenness of sheen, texture, and uniformity of application among other things (depending on the specifics of the finishing formula). One way to see problems that don't immediately jump out at you is to look across the piece into a soft, raking light. Defects in the film that you never noticed will scream out loud. Having said all that, the most important aspect of a refinishing job is its long term durability. Unfortunately I don't know of any way to definitively tell when a finish will fail prematurely just by looking at it. There may be indications in the general workmanship that might speak to the professionalism of the guys doing the work (runs and sags, orange peel, over-spray, etc. etc.) but that's not a guarantee. Not to mention that if you're seeing these things, the work is already done and therefore the damage is already done. I would suggest looking for these red flags before the work begins:


The vibe: Typically when you contact a company to do work like this, the process begins by them sending out an envoy (often the owner/operator) to come and asses the situation and give you the homeowner an idea of what to expect in regards to time frame, budget, and start date. If you get a bad vibe during this meeting, that's a red flag. Trust your gut. Also if you're taking bids and one of them is half the price of the others, it is not a bargain it is a red flag.
Appearances can be revealing: A crew that shows up wearing nice uniforms (even if they're just matching t-shirts and painters overalls) in lettered company vehicles is a crew that has it's collective poop in a group. On the other hand if the workmen, or worse yet the boss, show up dressed shabbily in a battered junker vehicles, that's a red flag. Guys that are good at this make a descent living and they tend to invest that back into their company. If they look like they're near poverty there's probably a reason for that.
Investigation of the preparation: When your crew is done prepping the site, you should be impressed (maybe even stunned) with the thoroughness and tidiness of the masking/tarping job. It should look like a patient prepped for surgery. If the masking paper is haphazardly applied and your floor is tarped off with old bed sheets, that's a rouge drapeau. That's "red flag" in french.


Hope this helps, cheers!