Part of the risk of a any drug is that you might be alergic to any ingridient. If you take multiple different drugs with ingridients, there's a higher chance you increase the chance of being faced with an ingridient that you have a bad reaction towards. I don't think that's a huge concern in this case.
One problem with taking the same vaccine multiple times is that your body might build defenses against ingridients in the vaccine besides the spike peptide which makes the second dose less effective. As far as I remember the Russian vaccine uses different virus vectors for the first and second dose to counteract this.
Given the situation we have in Berlin where we have at the moment more AstraZeneca vaccine, I got AstraZeneca as the first shot. My doctor recommended the BioNTech vaccine for the second shot because it might increase protection against new strains like the South American one. While giving that recommendation my doctor didn't think there were any risks regarding mixing that were worth telling me about.
I think the difference in risk are likely tiny between mixing and not mixing. I would expect that it's more likely that mixing is reducing risk then increasing risk.