The scratches in the print you saw would have all come from poor projection. Prints from the lab typically should be pristine and free of scratches. Mag scratches would for instance probably have prompted a reshoot or rescue with wet gate printing.
I saw 'Once Upon A Time In The West' in 35mm about 12 years ago (Curzon Mayfair) - it looked pretty good at the time. Its possible you've seen the same print with another 12 years of wear and damage.
Typically black scratches are on the base side of the print. Coloured scratches (normally) green are on the emulsion side of the print. The colour of emulsion scratches is dependant on the depth of scratches as they cut into the emulsion layer. Diagonal scratches come from badly setup long play platters. Typically scratches and general handling marks are worse around reel changes (every 20 mins or so).
You often get different scratches from change over houses - e.g two projectors are being used and one projector is good and the other is bad. you can have a situation where every odd or even reel is scratched. I've seen that some times. Also you get prints that are assembled from the best reels the studio has. So they may go through 10 damaged prints to put together 1 ok print. Which could result in very uneven looking prints. The UK 35mm prints of Bladerunner I've seen are like this. Generally terrible but 1 or 2 reels that are somewhat ok.
The source of scratches on projection are often due to either badly set up projection tension forcing parts of the film to rub against things. Also cleanliness - films shed and that gunk can build up in the projector gate and cause scratches. General dust and atmospheric dirt can also get on the print.
Of course now film projection is so rare there are going to be less experienced projectionists around so damage is probably more likely. The Hateful 8, 70mm run had lots of problems due to inexpereinced operators running and ruining film
Really the booth needs to be a very clean room. If you've ever seen an IMAX film booth they are kept pristine and the image on screen is a testament to that. Its rare to see dirt and scratches in IMAX film projection
In some cases when a print has been built up and broken down for projection many times - the ends get damaged and frames go missing. Eventually it can mean the change over cues get chopped off and projectionists make their own change over cues by scratching X's on the print or using a hole puncher.
With good handling 35mm can look great and their isn't an excuse for scratches since they all generally come from poor film handling, poorly set up projection equipment and general booth cleanliness.
Wading through www.film-tech.com can result in some insights - you'll have to search the archive though since they don't discuss film projection as much as they did.