There are potential hazards like with human vaccinations, but less generally can go wrong.
The possible problem with myxi is just generally a localised reaction (it might get red and sore if not massaged after in injection properly) although it can make them feel a bit rough so lots of tempting with their favourite foods. I have seen a bunny where it obviously stung and so he scratched it and made 50p size wound, followed by a scab, so you would need to watch for that, and then act accordingly in that happened (i.e. bathing the area). I've personally never had a problem with the myxi at all and with all my buns we have gone through a lot of myxi vaccines.
The VHD jab can potentially have more problems, but given VHD can kill your bunny without you noticing they have it, it is worth it. It can give the 'Cylap limp' if it's the Cylap vaccine, but this should ease (there are two, Cylap and Lapinject). They can also get a localised reaction. I also had a bun who lost a lot of coat and went bald due to the vaccination (this only showed a week and a half after). All the problems I had with mine we worked out occured in the smaller buns, and now, for any rabbit under 1.7kg they get a half dose of the vaccination and that covers them the same as a full dose covers larger rabbits. We have not had any adverse reactions since sticking to this rule.
If they get a red, sore localised reaction you can use a smear of Sudacrem on the area and that should help.
The benefits outweigh the risks in both cases, you just have to give them some TLC the day of and the day after and make sure they are eating and pooing. The risks are far minimal compared to what the actual illnesses can do.
Hope that helps.