Motion components
(X and Y-axis) Symptoms of failed, misaligned, or loose belts
There are two belts on the Ender 3 Pro. The X-axis belt drives the print head from left to right and the Y-axis belt moves the print bed back and forth. If one of these belts becomes loose or otherwise misaligned, you'll wind up with layer shifting, where it looks like a print has been "sliced" and shifted off its intended axis. The direction of the shift will indicate whether it is an X or Y-axis issue.
Adjusting the belts
The correct tension should allow the belts to plucked like a guitar string, but not so tight that they generate a high-pitched tune. Slightly loose is safer than too tight, as this printer is generally fairly slow. If you upgrade the motors to higher amperage units, you may need to up the tension.
In either case, you'll need to tighten the belt for that axis. The concentric nut that tensions the belt is oval-shaped on the inside, which is where the tension comes from. Cranking the nut to the right will typically tighten it, but if you go to far, you can tighten them going left, as well. You may need to loosen the retention bolts near the concentric nut in order to tighten the belt. Loose re-tighten the retention bolts during tensioning and pluck the belts until they sound tight enough.
(Z-axis) Symptoms of mis-aligned or dry lead screws or binding couplers
Behind the gantry towers, you'll find two long threaded rods - the lead screws. At the very bottom of those rods, you'll find the couplings that attach them to the Z-axis motors. I have found that on this printer, they sometimes over-tighten themselves and need to occasionally be loosened. These may need to be replaced at some point.
If you find that either one side of the Z-axis won't go up, or that the gantry is not sitting evenly, or becomes uneven during prints, you may have an issue with these couplings.
When I first got the printer, things were printing "squished" (a 20mm calibration cube measured only 14mm tall, for example), while the width and depth remained consistent and more or less accurate. This was due to BOTH couplings being incredibly over-tightened. I assume that this is what drove the guy to get rid of it in the first place, and it was a 30 second fix.
Adjusting the couplings
Simply turn the rods by hand (not by the couplings, by the rods themselves) until you can access the allen bolts holding them in. First, break them loose (they tend to get way over-tightened on their own) and then just snug them back on. You should be able to slowly rotate the couplings to move the lead screws. Do the same for both sides, to make sure tensions are the same on either side.
Lubricating the lead screws
Another issue with this machine was incredibly jarringly loud movements on the Z-axis. Find any synthetic grease to use on these. Simply apply it to the rod just above or below the gantry, and then run the Z-axis up or down slowly either using the on-screen controls or through Fluidd. DO NOT USE WD-40 FOR THIS - it is a penetrating oil with poor lubrication qualities and will in fact displace whatever lubricant is left on the screw. I have used Super Lube (Amazon link) or sewing machine oil, in a pinch. However, sewing machine oil is not recommended, as it's very thin and will dry out fairly quickly. For that reason, I also can't strongly recommend a dry lube unless you are fine with very frequent applications.
All lubes will cause filth to collect, so the less "globs" you leave behind on stuff, the less frustrating cleaning will be.
Non-motion components
Build plate
Symptoms of a dirty or damaged build surface
Every build plate will get filthy and eventually be ruined. The magnetic sheet that comes with the machine should be treated as a disposable unit and will need to be replaced fairly frequently. Other types of build plates may not need to be replaced as often, but most will need to be cleaned. If lines look to be coming out evenly but hot filament simply will not stick to the surface of the build plate, your surface most likely needs to be cleaned, or in the worst case it will need to be replaced.
Types of build plates
Magnetic mat
The magnetic mat, like the one with the machine, is a very good build surface with a very poor lifespan.
Remove prints from the bed by simply peeling the plate off of the heater bed and then carefully pulling the mat away from the bottom of the print. When needed, scrape prints or stubborn filament off it using a plastic tool to maximize lifespan.
Spray with 90% rubbing alcohol and wipe down with a clean microfiber towel between prints. If something is sticking badly or if alcohol isn't doing the trick, clean with dish soap. If the surface becomes damaged enough that a print won't stick in a certain place, you can extend its life by putting blue painters type on the surface of the bed to even out any valleys on the surface.
PEI plate
My preferred build surface is a PEI plate. The one I purchased from Creality was an absolute dud, though.
PEI plates are also magnetic, but they are applied to a spring steel sheet so that prints can simply be "popped" off of them. They also get to temperature very quickly and can also either leave a pleasing textured bottom when using the textured side, or a glossy reflective bottom when using the smooth side.
The same cleaning and maintenance apply to PEI as they do the regular magnetic sheets, but you can use metal tools on them without major concern assuming you don't go at them with a steak knife. Still regularly wipe them down with alcohol and clean with dish soap when needed, however. PEI plates are far more durable but also require a more finely tuned machine to get prints to stick to them.
Glass bed
This is the classic Ender 3 print bed that you'll find people talk about using gluesticks and hairspray on. The benefits are that you always definitely have a flat build surface (although you still need a bed mesh in case something is slightly tilted - but you can really trust the accuracy on that mesh), and there are a lot of people on the internet that will help you sort out issues with it. I've never used one, but the same cleanings seem to apply - you just need to be extra careful not to break them. The blue painters tape trick seems particularly common for these, and obviously if you're using hairspray or glue sticks, you need to clean much more.
G10/Garolite
I haven't used these before but Tom swears by them. It's basically a special kind of fiberglass that, once sanded a little bit, apparently can be veeerrry sticky. Ask Tom about this if you're interested, I have no idea how to take care of them.
Fans
There are several fans on the machine. Systems fans are in the control box in the pink & white box at the rear and in the PSU. You can blow these out from time to time, but they don't seem to be a high-failure-rate component. There are also two very important fans on the extruder itself.
Symptoms of failed extruder fans
The front-facing fan is the main hotend cooling fan. It basically runs whenever power is going to the extruder, to keep the hotend from having runaway thermals and melting filament too far back. If a print begins fine, but after a while filament stops being extruded entirely, you might be experiencing "heat creep," where filament has melted too far back, and then the extruder motors are just spinning around molten filament instead of pushing cool filament into the extruder.
The side-facing fan is the parts cooling fan. Different types of filaments need different cooling, so diagnosing issues at this point is quite a bit harder. If the fan DOES turn on during prints, you know it's working fine, but you may have other issues, but the worst is curling overhangs, where filament either cools too quickly (common if running a fan too high on high-temp materials like PETG or ABS) or if it doesn't cool quickly ENOUGH (common with PLA with too-fast layer times or too-slow of a fan speed), leading to curling filament that can get snagged on the nozzle, knocking over the entire print.
With how the wiring is on these hotends, if one of these fans fail, the only easy solution is replacing the entire hotend, which at that point you should probably just upgrade to something other than the stock Creality job.