So regular old 120v 15a and 20a circuits are really pretty concerning when it comes to EV charging. They are generally daisy chained from one receptacle to the next (either through the receptacles themselves, or pigtailed). If *any* of the connections is loose or not done properly this will result in resistance which results in lower voltage for you and heating for the the bad connection location.
NEC of course dictates that any EV charging plug be a single receptacle dedicated for that purpose. So nothing is wrong with 120v charging per-se, but it is supposed to be a dedicated receptacle on a dedicated circuit.
Now with that being said, we have all probably plugged into whatever random circuit was available at times without really knowing what else is going on with that circuit, while not optimal, sometimes it is the only option.
Depending on how much folks will let me do to their electrical system, I will typically first use a circuit locater to figure out which actual breaker a receptacle is on. Before that actually, I often try to chose a receptacle that is as close to the breaker panel as possible to increase the chances of it being the first receptacle in the chain (actually, ironically, often times this is a GFCI unit since those are installed upstream of all the other receptacles to provide the downstream protection. Then I will often remove the breaker panel cover and throw a current probe over the circuit in question. This lets me help figure out what else might be using the circuit. If I am lucky, I am on a 20a circuit (even if the receptacle is only 15a). That often allows for some headroom in case there is say a freezer in the garage on the same circuit. Maybe I only draw 12a (due to 15a receptacle) and then that leaves 3/5 amps of headroom for other loads (of course I have also been known to use my cheater 5-15 to 5-20 adapter and if I know the circuit is otherwise empty I can draw up to 16 amps off it).
So while I would generally not ever encourage folks to rely on a 120v circuit for their home charging solution, if you need to do this for some time period I would do the following: Try to figure out which receptacle is the first in the chain from the electrical panel - use this one if feasible. If it is a 20a circuit with proper wiring gauge and breaker, you might consider swapping the receptacle from a 5-15 to a 5-20 and then you can get the Tesla 5-20 adapter and charge 33% faster. But you first need to figure out why your Tesla is having issues with this circuit. It probably indicates a real electrical issue. Most likely you have a bad connection somewhere. Start at the breaker and make sure the wire is clamped properly under the breaker terminal with the right torque. Then move on to the outlets on the circuit and make sure any wire-nuts (if pigtailed) or screw terminals on the receptacle are tight. It could be a bad receptacle too, so if that is the case, replace the receptacle (they are only a few bucks).
Here is the circuit breaker locator I have (it works shockingly well for something from harbor freight - just make sure to read the instructions):
Search results for: 'circuit breaker finder'
The old school way of identifying a circuit is to make educated guesses based on circuit ampacities and labels. Then turn things off till you find the right thing. Then go around to all receptacles while the circuit is off trying to figure out what else is on the circuit. That might give you some clue to how the circuit is laid out.