Is a 1.0 mm thickness for a 4-layer PCB recommended or even common?
You won't experience problems with vias: 8 or 10 layer boards 1.6 mm thick are common, and then the individual layers are thinner than a 4 layer board of 1.0 mm thickness.
A 1.0 mm PCB will be less stiff than a 1.6 mm, but unless you want to place a heavy transformer on it (don't!) this won't be a problem either.
Standard thickness panels may be up to 635 mm (25 inch) wide, but your manufacturer will limit that for 1.0 mm thickness. Ask him how wide a panel may be.  

Overall, a 1.0 mm board is a bit less stiff, but for boards up to Eurocard format (160 mm x 100 mm) I wouldn't worry about it.