Can flashing your headlights lead to penalty points or a fine?

Answer: Yes
So a simple act of flashing your car headlights to tell another driver, cyclist or pedestrian to proceed, which you may feel is a freindly gesture to other roadusers could end up costing you a fine of £1,000 or 3-points on your licence. 
The Highwaycode says you should only use your car headlights to alert other drivers of your presence and not any other message.
The actual chances of being fined or penalised for doing this is highly unlikely and actually I don't know of anyone who has been fined for this. 
But the findamental reason for this is that simply flashing your headlights could convey any number of messages or meaning which could and may be wrongly interpreted by other roadusers and in itself could cause an accident.

Other reasons why some motorists flash their cars headlights
Some motorists also use a flash of the headlights to warn other drivers of a speed camera or police check point.

And in this case you are potentially breaking the law as this could be construed as obstructing a police officer in doing their duties. Therefore you could be accused or a criminal offence. The maximum fine for obstructing a police officer is £1,000.

Can waving at other motorists lead to a £1,000 fine?

What is deemed by many drivers as a nice act or friendly gesture the simple act of taking one of your hands off the wheel could lead to you receiving a £1,00 fine or points on your licence. This is becuase the Highway code states you should drive with both hands on the wheel of your car. If you do not have both hands on the wheel you could be deemed and not being in control of your vehicle. So even a simple thumbs up or a gestured thank you could potentially lead to a fine. 

Many roadusers have pointed out simple problems with this especially if you drive a manual car. And have asked how do you shift gears then?

Again there is a very small chance that you could be stopped and or fined for this but it is worth noting, especially if you are making an insurance claim and this evidence comes to light.
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Warning: THESE ACTIONS COULD LEAD TO YOU FAILING YOUR DRIVING TEST

If you are deemed not to be incontrol of your car by taking one hand off the wheel this could be marked down by your examiner a minor fault on your driving test and if you do this repeatedly or make enough other mistakes you could fail. If you make 16 or more minor faults, you will fail your driving test.

What are the most common driving fines?

Whilst the above acts or gestures are unlikely to get you slapped with a driving fine here are the most common reasons to get fined whilst driving.

1. Speed Limit Offences,
2. Car Insurance - Having no insurance or including being disquallifed for driving,
3. Driver Identity - Failure to provide or prove your identity,
4. Under the influence - either drigs or alcohol or failing to provide a specimen of blood, breath or urine,
5. Other motoring offences - surround safety including vehicle in unsafe condition, using mobile phone and also failure to stop after an accident,
6. Vehicle tax and registration,
7. Failure to adhere to the rules of the road (not speeding),
8. Driving Licence,
9. Dangerous driving- including driving without notifying the DVLA of any disabillities or medical issues which may make your driving licence invalid.