One issue when using J1772 EVSEs that some people have encountered is
melted J1772 adapters. AFAIK, there's no definitive/official explanation of the cause, but my own hypothesis is that something has degraded the contacts in the J1772 plug (maybe dirt or corrosion), and this has reduced the conductivity, resulting in increased heat generation. As the J1772 adapter is a dumb pass-through design without its own heat sensors, the Tesla can't know that anything is wrong, so the J1772 side of the adapter can melt. I have noticed that an awful lot of reports of these problems mention that the station provided 48A (as is common at Volta stations), which suggests that the problem is more common at higher amperage than at lower values. Most public Level 2 EVSEs max out at 30A or 32A, so if my hypothesis is correct, they're less likely to overheat badly enough to melt the adapter if there connection is slightly degraded.
Supercharger stations don't involve adapters, so the Tesla's built-in temperature sensors are more likely to detect problems and reduce the charge rate with them. The new CCS1 adapters are new enough that it's not clear if there might be problems with them from time to time.
Overall, this implies that examining the contacts, as
@Tronguy suggests, and cleaning them with compressed air (or just blowing on them), as you yourself suggest,
@Bankmaggot, are good practice, particularly when using an adapter.