There really is one place to appeal to in the light of injustice and that is to the Queen via her Council. This has not so far been done for traffic offences as it is widely known the Queen hates traffic congestion, careless flying and so on so it is assumed it is best to take whatever punishment the fairy squad see fit to hand out and get it over with. The Queen does not mind this at all!
However there is the Court which she heads when it comes to magical crime as a whole and it is felt it is only a matter of time before some incident involving traffic control ends up here. She has urged her fairy squad to make sure they cannot be sued for anything. Hanastrew would like to see anyone try that - she always was game for a decent magical fight.
The biggest one is speeding. The second is careless flying. The third is flying without undue care and attention (the witches are particularly bad for this). The fourth is careless behaviour by a pedestrian which covers everything from suddenly stopping dead in the middle of the High Street to veering around and whacking the person behind you who was not expecting a sudden change of direction.
Pedestrians are expected to be considerate to all around them including those behind them (and one good side effect of this is the mass reduction in pickpocketing as with people being more aware of those behind them, they are less likely to fall victim to this). Pedestrians are welcome to report incidents that have happened to them. This usually involves careless flying and the pedestrian in question getting a broken limb or two as some junior fairy or witch still trying to get used to their flying machine overestimates their ability to control it and crashes into some poor sod beneath them.
Drink driving is an issue at celebration times as it is on Earth and the fairy squad clamp down hard on it. Offenders usually get a decent dipping in the nearest water trough before spending a night in the cells. Given the water troughs are always ice cold (made magically so given the Kingdom's climate is generally mild), most offenders do not come back for a second go.
Magic mushrooms are generally used as a spell ingredient and if you're on the receiving end of that charm, it is highly unlikely you'll be driving anything for some considerable time (and possibly permanently if the Witch performs the spell). Littering offends most species in the Kingdom (the exceptions being the sprites who get zapped by the other species if they're caught doing this).
Overtaking offences only apply to the road - if flying it is expected that folk will ensure there is plenty of room to do the manoeuvre safely. Get it wrong and you will be the one tumbling from your broomstick or other flying vehicle of choice at several hundred feet up. That kind of fall will hurt.
Practicing magic in a prohibited zone. This usually means anywhere near the Palace. The Queen gets twitchy if she senses witches or wizards brandishing magic anywhere near where she lives. She also believes it holds up traffic unnecessarily. She is right on both counts. The penalty for disobedience here is death by instant zapping by the fairy squad. They query why anyone would want to practice magic near the Queen's major residence and refuse to believe there could be a good reason for it.
The misuse of mirrors. Mirrors are meant to be attached to flying vehicles and to be used in a similar way to those on vehicles on Earth. However, mirrors are often used to reflect magical power, sometimes to even intensify it and again the Queen and her Council take the assumption anyone doing this cannot possibly be up to any good so give the fairy squad free range to tackle offenders. Again offenders are unlikely to repeat the offence (it is difficult to do so when what's left of you is a smoking pile of ash).
Creating traffic hold ups/causing problems on the road for other road users. Known as the Audi/BMW Gambit (by Jenny when she discovered the Fairy Kingdom's Highway Code and wanting a parallel with life on Earth), this kind of behaviour is not tolerated in the magical world. Sprites, known for their mischievous streak, were the best known for this but got tired of seeing their colleagues being zapped for it so this is not the problem it once was. The Queen wants it to remain on the statute books however to ensure the sprites continue to know if they go back to their bad old ways here, so will the fairy squad who are amongst the finest aims with wands in any known dimension.