Hi Meebh.
Putting dirty eggs into an incubator will contaminate the incubator and all the other eggs.
Any virus present on the egg will multiply under these almost perfect conditions and infect the chicks.
Washing them makes it worse, as using anything other than dry removal will result in the egg shell allowing germs through into the egg. The pores of the eggs will get blocked and problems with oxygen/carbon dioxide may arise.
Try to collect when the ground is dry and remove eggs that are going to be used for hatching as often as you can from clean nestboxes.
I know this all sounds over the top, but whats the point of asking for hatch problems by setting contaminated eggs.
If you have to wash eggs use warm water, as using cold makes the inner membrane contract and more germs are sucked in.