As long as we're talking about an actual needle with the dedicated purpose of being used for injections, I really doubt that there would be any complication. Veins are fragile and easily destroyed, while by comparison, the muscles are pretty robust. It's not likely that you're going to cause serious damage with just a single injection. With an elderly patient, there's going to be less bounce-back in terms of the tissue repairing the hole left by the needle, but I doubt it could cause a complication.
Are there symptoms? Pain, redness, swelling, other complaints?