Although the subject of rule changes in F1 is often a contentious issue, especially recently, one rule change I would like to see implemented would be that similar to the IndyCar system where points are awarded for pole position and the fastest lap in a Grand Prix.
Even if it was only three points for pole and a couple of points awarded for the fastest lap I think that there are serious merits to the system.
Firstly, if you start on Pole but for some reason or other do not finish the race it would at least mean that the weekend has not been a complete loss, particularly given for that in effect by gaining pole you have won one of the two competitive days of a race weekend. If you gain pole and win the race, then a driver / team would receive an extra reward for total dominance.
The award of points for the fastest lap I believe would help liven up races, particularly as we have seen on many occasions where at the latter stages the result is often a foregone conclusion. It would provide an extra incentive for drivers in the middle of the field to at least keep racing until the end of the race if there was a chance of gaining some additional points, while it would also provide the incentive for a team who was considering retiring a car to save parts for future races to at least stay out if they think they have a chance of achieving the fastest lap. It might even encourage a team to fix a car to get it out later in the race if points were on offer for the fastest lap.
While I’ve not done the calculations to see what the effects would have been had this system been in force for previous seasons, and ultimately I don’t think it would have a major effect on who wins the championship overall (for most seasons), I think this system could provide some extra entertainment in a Grand Prix and provide some of the mid table teams a chance to pick up some extra points during a season.
Lastly on the subject of points, I would like to see (and I know I’m not alone with this view) a rule which replaces the double points system at the last race of a season replaced with the opportunity for a driver to play a wildcard at any track during the season (before the start of the race weekend) so that they could gain double points at a track which they felt strongest at. While I’m guessing that double points for the last race was introduced to keep the championship alive for longer, in my opinion providing the driver with the opportunity to score double points where they think they would be strongest would be a much fairer system. Just a thought!