Two questions

Slates probably refers to which take it is. An audio recording would have a little speech at the front that would say, "Track three, take two," or something like that. So what the booklet is saying, I *think* is that they had a sheet saying where the sounds were from but the recordings weren't "slated" properly, so they don't know which "take" they're from. I'm shooting in the dark a little there.

Multitrack means that all the parts are recorded on their own "track" and are mixed from there. So, if we took a typical rock band, there'd be one track for the lead guitar, one for the rhythm, one for the bass, one for the drums, one for primary vocals, and one for secondary vocals. They might put some instruments on the same track or have more tracks for extra instruments or overdubs.

When they mix from a multi-track, they would carefully balance each, separate element to get the optimum sound out of the whole thing. Depending on available tech and how meticulous they got, there could be a LOT of tracks in an orchestral
score for a film. At first, "tracks" weren't really a thing until 4-track and 8-track recorders were invented. They could have had 20+ tracks, depending on what was going on in the recording studio.

I think 2-channel stereo is redundant, since "stereo" basically means "2-channel". It means that they put some of the sounds in the right speaker and some in the left. Usually by recording with two microphones on the right and the left. This approximates the sound of the live band/orchestra.

So, basically, if I'm reading this correctly and if I've got my terms all right (I'm not a pro or anything) they saved money by balancing the left-right speakers to give a good, stereophonic mix, but they didn't bother going into master tapes of all the different tracks and rebalancing the sound for modern formats; they just left the mix as-was and messed with the stereo.