Appearance is a large part of the appeal of vintage audio. Some equipment was made with handsome wood cabinets, decorative metals were used and plastics had colors and shapes styled to a different age. Analog meters and dials were the norm; digital parts were uncommon until the 1980s.
Wood and older plastics have safety issues such as fire and smoke hazards. Plastics found in older equipment can be brittle, yellowed from age or otherwise deteriorated.
You can find specialty suppliers for many vintage parts on the Internet. They stock tubes, knobs, variable capacitors and other items. Some parts, such as CRTs, may be much more difficult to find. Other parts, like resistors and capacitors, can be replaced by modern equivalents from your local electronics store; the results will be identical.
Many audio components made in the 1970s will still sound good today, provided they're in good repair. Much older than that, equipment will sound noticeably different; system and part designs were less advanced than they are in 2009. The expectations of audio fidelity were lower at the time. In particular, high- and low-frequency reproduction won't be up to modern standards, the sound will have more hiss and hum, and the range between the loudest and softest sounds will be more limited. For many, this is the great charm of vintage audio--the sound quality is nostalgic.
Though getting vintage parts might be chancy, electronic repairs on vintage audio equipment are generally simple. Component density is lower, and hand assembly is more prevalent. As with repairing any electronics, be careful around high voltages. Vacuum-tube equipment in particular use in excess of 200V.
Mechanical and cosmetic repairs will be somewhat more difficult than for modern equipment. You may need to make your own replacement pieces from wood, plastic, or metal.
If you're not up to repairing equipment yourself, some repair shops specialize in vintage audio. It may mean sending your gear out of state for servicing, but knowing an experienced technician is doing the work is a big plus.
Since all vintage audio is used, prices will vary by condition, make and what the seller thinks she can get. Plenty of bargains can be found if you're willing to overlook a few blemishes. Fussy, meticulous sellers will offer a spotless item at a high price. But for other than museum-quality gear, prices will be comparable to or less than new equipment.