When I plug in a vacuum cleaner in some rooms the lights dim, in other rooms this does not happen. Is there some type of problem with my wiring

Very difficult to tell if this is a problem from where I'm sitting...
Do the lights dim a little? 10%? 20%?
It is common and OK for lights to dim "a little" when a large load is applied
To the electrical system... however if you think they are dimming more than a little
Calling a good electrician can make sleeping easier...

Vacuum cleaner motor draws a lot of power. If you have a lot of lights or other appliances on, it will reduce the power i.e. drop the voltage.

Agreed, some vac draw 15-20 amps which will pull down that one circuit, that can dim the lights if they are on the same circuit with the vac outlet. The other rooms the lights may not be on the outlet circuit. This isn't a real new home is it?