Oh yeah, I'm going to be replacing the caps.
In that time the solder masks and manufacturing processess weren't as perfect as they are now. There's probably tin on the copper layer under that area of the soldering mask. The solder mask might come off very easily there, but it's cosmetic and the copper is protected by the tin, which isn't very reactive and won't really be affected by moisture etc. nearly as much as the blank copper would be. It's sometimes hard to tell from one picture, but that does not look like corrosion or damage. Check if any ICs and passive elements have anything green on them.
From memory:
Capacitors I wouldn't bother replacing on these old A2000 boards, they're probably still good to go. I would replace all capacitors in the power supply though, if you trust yourself to do that. You might want to replace the X capacitor too, while you're at it, some of them in power supplies of that vintage are prone to failing and that's not very safe and also unpleasant (very bad smelling, scary smoke) if it happens. If you have one of the older Amiga 2000s, the power supply will be made in (west)germany or england. I would keep that power supply, it's built like a tank and after a recap will easily last another 40 years. (Not power efficient though) The later ones are made in china, and nothing special. The early power supplies had capacitors that were prone to failing after ~5 years, there was something wrong with them, so it's kinda important to replace them, there's no POWER_OK or anything like that (like in ATX) in these power supplies and it can totally damage your Amiga if they don't work correctly. Also when testing, don't turn it on if it's not connected to a user, (mainboard, old filament bulb etc.) it can break the power supply.
I think in the older style power supply the net filter (x cap) was integrated into the power plug. I could probably get you a spare part number if that's the case for you.
While you're at it and think about replacing the fan with a quieter one, be aware that IIRC it wasn't a normal 12V fan in the early power supplies, but a 110V one. Contrary to modern power supplies, the 12V rail is more of an appendix in these and basically used for almost nothing, so you can't put a big load on them. If you really have a video toaster, you kinda want to keep the original power supply as the Amiga derives the TICK signal from the power networks' frequency from it. There are better solutions for that today though and it's not a total showstopper if you wanna replace it, as you probably don't plan to synchronize to late 80s studio equipment. The Video Toaster is very touchy about that signal missing though and some of the older A2000 boards also need to have a jumper set if the signal is missing IIRC.
Re: 12V. Modern power supplies are regulated around 12V and that's their main line because of modern point-of-load reagulation, this old Amiga supply is all about +5V. If after reading all this you plan on replacing it with a modern power supply, be aware that this is not ideal for the modern power supply, as in most modern supplies the +5V is the appendix for legacy purposes, and it actually might not deliver enough ampere in a fully-expanded A2000. It's also a very bad way to run a modern supply with no load on the +12V and all the load on those +5V and it's not good for it. The negative voltages these computers needed for some exotic purposes (e.g. modem) are also usually missing in modern supplies, and there might be lots of ripple on the +5V the different revisions of A2000 mainboard are not good at catching.
Good machines. First computer I owned, bought it in 1987. Mine is still in working order and has a Merlin graphics card and a Blizzard 2060. Ran a BBS on it in the 90s. Desktop cases are where it's at.