OP isn't specifying a country, so I'll speak for Germany. There is no part of the StVO (Straßenverkehrsordnung, road traffic regulations) which gives rise to a civilian becoming a "traffic enforcer".
Hence, you would be best served by not breaking any law yourself when witnessing an offender. The safest bet would be to report the event to the police and record and provide evidence, hoping that they will take care of it. If for whatever reason you decide that it's a good idea to follow the other car, you'd still need to move within the speed limit, and you cannot simply decide to hinder them, push their car to the side or anything like that.
This kind of responsibility (i.e. to apply force to a fellow citizen) is (at least in Germany) clearly regulated by laws related to the Verkehrspolizei (traffic police) together with regular police law.
As an example for where the law makes this clear: if you are a Schulweglotse (a person with a yellow coat and a flag, helping school children to cross roads safely, often at busy traffic lights), the relevant law clearly states that although you have to be trained by the police in your job, you can not regulate traffic in any way, shape or form. For example, when you get this training, you are clearly told that if "your" traffic light has an outage, you are not allowed to regulate the traffic flow (much less do anything about any offenders).
So, TLDR: since there is no law in Germany making you a "civilian traffic enforcer", and since the opposite is explicitly stated in the few edge cases where other laws could be interpreted that way, the answer to your question is "yes" - if you do something illegal while forcing a potential wrongdoer, then you are liable just like anyone else if push comes to shove, and are putting yourself at the mercy of the courts.
Note that all of this says nothing about ethics or morals. Obviously, you can construct extreme cases where you can or maybe even should, as a good human being, decide to do whatsoever you wish, while accepting the consequences (i.e., whatever the law may or may not throw at you at the discretion of the court).
PS: Note that a dashcam is not allowed in some countries. I.e., in Germany, not only is dashcam evidence not admitted in court, but it may even be held against you due to the cam conflicting with EU privacy regulations.
PPS: Just report that Mustang if you recall the license number. If the driver pulls several such stunts, and other citizens report them as well, then over time the police might just pay them a visit; or if they get involved in an accident later, having such reports may count against them indirectly, in court.