The cassette that Frasier has in his cabinet are of a type that typically have 60-90 minute capacity per side. And since his radio show is three hours long (180 minutes). One tape wouldn't be enough to store even one show. Much less the more than three per cassette that would be necessary to fit 2000 shows on 649 cassettes.
When Frasier is in the records room he states the tape that's missing is from 1993. In the next scene, in his broadcast, he states he's looking for a tape from 1996.
When Daphne confesses to ruining Frasier's tape, she says she put a screwdriver in her boombox to try to get the tape out, which "broke the tape." Cassette repair kits were available at the time. All one needed to do was take the tape out of the broken cassette case and transfer it to a new case, and the tape would be as good as new. If the tape itself was broken, special clear adhesive tapes could be applied to splice the tape together.
When Roz and Frasier are in the archives looking for old Frasier tapes, Roz finds a box she calls "Best of Crane." But on the side of the box, it says "The Frasier Crane Show."
However, the side she views is not seen by the camera. It is possible that a different name was on the side facing Roz, while the outward side seen by the audience was labeled "The Frasier Crane Show".
It appears throughout that each of Frasier's tapes are for a single episode of his show and all the tapes are in one cabinet. The tape that Frasier puts away claiming to be his 2000th is actually the 841st tape in the cabinet. In fact, it's the 840th tape! there is one tape missing in the lower right corner.
After Niles (David Hyde Pierce) takes a picture of Tom (Adam Arkin) and Frasier (Kelsey Grammer), Tom looks at the Polaroid and says that Niles' thumb was in front of the lens and insists he take the picture again. But as he hands the picture to Niles, you can clearly see it's still grey, having not fully developed yet.
Frasier mispronounces "amphora."