Is a mix of copper and galvanized pipe a problem if dielectric unions are used where they meet?

Dielectric unions reduce the rate of galvanic corrosion that occurs when dissimilar metals are in electrical contact. They don't eliminate it but they slow it down. How much does occur also depends on the mineral content of your water.

You should always use a dielectric union when there is a transition between one metal and other.

Dielectric unions are not needed between metal and any type of plastic pipe.

As has been stated combining copper and galvanized requires a dielectric union between them to reduce galvanic corrosion.
However, to specifically answer your first question:
As long as dielectric unions are used where they meet, is there a problem with having both galvanized and copper in the same system?
The answer is no there isn't a problem but it also begs the question of which is better. Galvanized pipe has a higher propensity to corrode than copper causing leaks and taste issues whether or not it's in contact with copper. Galvanized was used in many homes prior to 1960. So if you decide to go with one over the other I would choose copper over galvanized. Builders today usually go with Pex over copper because of cost issues (material and labor) so that's also a consideration.