I have a 2002 Itasca Suncruiser 35U which is virtually identical to the Adventurer 35U. My opinion, and that of many others, is that the 35U is one of the best floor plans that Winnebago has ever made. Although we haven't had time to use it much since buying in in Nov 2017, we love it.
We found the sofa to be a bit clunky and somewhat difficult to use and replaced it with two electric, leather recliners. Alternatively we could have replaced it with a double recliner or more modern sofa-bed.
We also replaced the old vinyl with luxury vinyl planking and the old shag carpet with commercial carpet tiles. My wife re-covered the dinette cushions and the valances. The day/night blinds, if you have them, can be washed in the shower with Clorox Clean-up Cleaner+Bleach spray. Ours' came out looking like new. The Clorox spray also works wonders on any leak stains on the ceiling headliner.
Another thing we did was to replace the old converter with a modern one with multi-stage charging. It's much more gentle on your batteries:
Plan on re-caulking your roof joints, vents, etc. and carefully check for water leaks. Our's had a cracked and repaired skylight that had damaged the bathroom ceiling. A new skylight is about $300. We also replaced the toilet with a more modern, high profile, ceramic toilet (less than $130) instead of trying to replace the seals in the old one.
Our biggest single issue was leaking hydraulic hoses so carefully check for signs of hydraulic leaks. Most of our front slide hydraulic hoses had leaking fittings. You can DIY but, if you have all the hoses replaced professionally, it can be $1,000 or more (hoses are cheap, labor isn't). I don't know if it lasted until 2004 but HWH (the slide out manufacturer) had a problem with hoses in the early 2000s. As long as the slides and jacks work OK, hose leaks aren't a cause for rejection, just negotiation.
As with any coach, make sure the major systems, refrigerator, air conditioner (heat pump), heater power management center, etc. are in good working order and that the "truck" part is in good shape (engine, transmission, brakes, etc.). Extremely low mileage like 12,000 can be a sign that the rig has sat unused for most of it's life without routine maintenance which can be an issue, so look for a reasonable mileage figure (our's had 56k). Check the DOT date code on the tires and, if they're several years old, negotiate. Six new tires will cost close to $2,000 or more. Also, unless they've already been replaced, plan on new shocks. If you can, get the "truck" part checked out pre-purchase by a good truck repair shop experienced in your brand of chassis (Workhorse or Ford). Major repairs, especially a transmission or engine rebuild can be reasons for rejection.
Here's a good site with a lot of tire-related info:
RV Tire Safety: Tire pressure Increase
If it has a Workhorse chassis, make sure the brake recall has been taken care of, or find out how to get it done:
(note: this is an old site since it says parts aren't yet available)
It should be obvious if it's been fixed since the calipers will look new.
Read up on the Winnebago windshield leak issue and make sure you don't have a major problem. Fixing a windshield leak can range from simple sealing/taping to $2,000 of rust/metal frame repair. This problem is not unique to any particular model or years of manufacture. This is the worst case:
Search winnieowners.com for more info. I was lucky, mine had already had the metal work repair but I still had to tape the top rubber gasket with Eternabond tape.
Most of the other "house" items, such as water pumps, shower heads, faucets, etc. are relatively inexpensive and are DIY.
I think the 35U is a great coach and would buy it again so don't be scared off by all the things I've listed. Most, if not all would be common to any rig more than a few years old. From what I've read and, based on my own experience, plan on spending $2,000 - $4,000 over what you pay for your motorhome to get it into shape.