"do the dishes" vs "wash the dishes"
Solution 1:
While the previous answers are correct in stating that you can use 'do', 'wash' and 'clean' interchangeably, I would argue that 'do' is a lot more informal. 'Do' used in this way is a little bit slangy. For example 'I'm going to get my hair done', or "We're going to a do at the Town Hall'. Note how in the latter example 'do' is used as a noun to mean 'party/event', and is very colloquial.
Oi Pete, can you do the dishes? [informal]
Excuse me Peter, would you be so kind as to wash the dishes? [formal]