I have been trying to research about the spectators of Circus Maximus. I know there were different colored factions. But my question is; "Were spectators able to throw items at racers to hit them or distract them and make them try and fall off their chariot?"
There does not appear to be any primary source evidence of spectators throwing things at charioteers at the Circus Maximus, but the Greek philosopher and historian Dio Chrysostom relates how partisans in Alexandria threw clothes at the competitors. On these 2nd century AD spectators he says:
When they enter a theatre or stadium they lose all consciousness of their former state and are not ashamed to say or do anything that occurs to them.... constantly leaping and raving and beating one another and using abominable language and often reviling even the gods themselves and flinging their clothing at the charioteers and sometimes even departing naked from the show.
Alexandria, along with Constantinople, was in later centuries to become somewhat notorious for violence associated with the circus but there is little direct evidence for the city of Rome.
At the Circus Maximus, spectators were certainly passionate about the races, with some writing curses on lead tablets:
The curse tablets (defixiones) were lead sheets engraved with magic symbols, formulas and curses....After the tablet was activated with incantations or sacrifice, it was rolled up and buried at strategic places in the track..
One such example is is cited by the penelope.uchicago.edu article Circus Maximus
"I adjure you, demon whoever you are, and I demand of you from this hour, from this day, from this moment, that you torture and kill the horses of the Greens and Whites and that you kill in a crash their drivers...and leave not a breath in their bodies."
Pliny the Younger's comments on spectators at the Circus Maximus are noted by Sinclair Bell in Roman Chariot Racing: Charioteers, Factions, Spectators:
spectators indulge their “childish passion” in the circus. Worse still, they allow themselves to become emotional and violent, and generally lose all self-control, even though seemingly nothing is at stake.
Pliny doesn't say spectators threw things at the charioteers, but we cannot rule out the possibility that a few spectators did so at times. However, what really drew the attention of writers in Rome was not so much violence as betting. Among these writers are Juvenal and Ovid.
In addition to betting, they also mention the dating opportunities provided by the circus as the sexes were not separated, unlike at the Colosseum and in theatres. Ovid
counsels his readers to exploit their cramped quarters to pick up attractive female spectators: “Nor let the contest of noble steeds escape you; the spacious Circus holds many opportunities”
are for the young, whom it befits to shout and make bold wagers with a smart damsel by their side
Alan Cameron, Circus Factions: Blues and Greens at Rome and Byzantium
It's not entirely impossible, but consider the situation as it was in Rome. There was no public prosecutor and no police. Yes, there were the Praetorian guard and the Vigiles, but their main tasks weren't maintaining public order. The Praetorians were the emperor's guard and the Vigiles firemen. Maintaining law and order was an extra.
Justice was pretty rough back then. You had to do it yourself. Only very important cases came to court. Most other cases where handled in and by the neighborhood. Also consider that Roman justice was, certainly compared with our system, rather harsh.
Full blown riots occurred when supporters had disputes. So much so that occasionally the vigiles and or Praetorians were called in to quell the riots.
That's your background.
Now imagine someone throws something at one of the participants to hit or distract him. At least 1/4 of the spectators wouldn't be amused. Probably a lot more. Chances are that you'd be very clearly told not to do that. Hopefully you'd be alive after being chastised.
Chariot races were hugely popular, also by the emperors. Any idea what an emperor could do when a supporter would intentionally obstruct a race?