Can an electrical false contact in my house cause the bill to go up?

No, a bad contact is ljkely to do one of 2 things

1. Cause appliances to malfunction, lights to flicker etc.

2. Cause a short-circuit and trip a breaker.

If you think your electric bill is much too high you can buy a plug-in device to measure the consumption of every appliance that can be plugged in. That leaves lights and permanently wired circuits like heating, AC and burglar alarms. You can measure these by switching everything else off at night and reading the electric meter last thing at night and when you get up in the morning. That will give you a fair idea of the consumption of each appliance. lights are on two or more separate circuits, but lighting is such a small part of the average electric bill that all the lights you use at night probably won't use as much as the average plug-in appliance.

It's a good idea to check the consumption of 24/7 stuff like fridges & freezers, if they are not efficient they will burn a lot of money.

False Contact

?? What is a false contact? If you mean a poor connection in the panel it could raise the power use but you would notice other problems before like dim lights or flickers in the TV or buzzing or arcing in the panel.

Yes it can it is also a fire hazard.