There are a whole range of things that might be covered under “enhancements”. The OP asks about “expert” enhancements, which does at least avoid simple automated enhancing systems.
Enhance could be reasonably be broken down into three categories.
[ul]
[li]Those that seek to extract as much information out of the original as technology allows.[/li][li]Those that seek to create new information making assumptions about the nature of the subject.[/li][li]Those that seek to make aesthetic improvements to the content.[/li][/ul]
Clearly there is some blurring of the boundaries here.
Examples of the first kind. Film transfers done well will go back to the original negatives, scan them at very high resolution (8k if you are really lucky), apply colour corrections based upon the film stock and film age, and also fix defects in the film (scratches and worse). At the end of this process you have a copy of the film that is probably better than anyone ever viewed it. Scratch removal however involves inventing new information.
Authoring of the film to a digital medium, Blu Ray for instance, will resample the video down to 2k resolution, and may perform “enhancements” for the media. An obvious one is to remove film grain. Another issue is the colour space of the film. Your TV has a different colour gamut to the original film. Removing grain is controversial - purists feel it is part of the aesthetic of film and should not be removed. Also removing it is never side effect free. It may blur detail elsewhere, and may also lead to strange visual issues in the area where the grain has gone. The colour space is a mix of technical and artistic choices. The original film may have been shot on a particular film stock for artistic reasons. If the transfer is done on the cheap it won’t be scanned at high resolution, nor will there be money to do all the nice colour grading and fixups. The authouring process may simply automate many of these, with automatic scratch removal, smoothing, edge enhancement, and a stock colour space. Edge enhancement is another case of creating new information where none was before. Done carefully it can add snap to the image, done badly and you get a new range of artefacts.
In the audio realm much the same is around. You can go back to a classic recording (where classic typically means something we grew up with) and rebuild the recording almost from scratch. If the 2" tracking tape exists you can almost reproduce the entire production. There are techniques that can extract more information off an old tape than the original recording engineers ever imagined was there. Tricks like sampling at 192 kHz so that the restoration software can see the bias signal, and use that to eliminate tape scrape flutter, and techniques that can correct for the exact physics of the tape formulation and recording head design. If you have the 2" multitrack is possible to recreate the entire mixdown again, and a new digital master of vastly higher quality to the original recording. Even if you only have the 1/4" master tape, you can still do really well here. However there is always the temptation to “re-master” the recording, which is an artistic call. Sadly this often means adding significant compression to “enhance” the punch and slam of the recording, and for many ears is a backwards step. (Counter intuitively, adding compression to a recording makes many people interpret it as more dynamic.) Even if you go back to the 1/4" master it is important to re-equalise it, since it will have been mixed for vinyl.
Noise removal is just like grain removal in films. You can do it, but it is never side effect free. How much, if any, to do is a mix of technical and aesthetic issues. If you go back to very old (like lacquer masters) many recording will still leave a great deal of noise present, as its removal leave a dead sounding recording.
In film restoration you need to meld the video and audio. A serious film restoration will seek as much original audio as it can, and rebuild it. But sadly often this is harder. You might only have an optical track to work with. Here it is probably a matter of doing as good a job as one can. But re-equalising, de-noising, dynamic band selective dynamic range expansion, and so on will all help. This is a case where the modern content delivery is much better than the optical audio track, and by making intelligent assumptions about the nature of the original a true enhancement may be possible.