Occasional extra counts when other wireless devices are nearby: heart rate monitors and the wireless computer of the person riding next to you. Also not a big problem.
My experience is that it is usually fairly big a problem.
Additionally at least some wireless models require that your start them when you start riding unlike wired models that just start on their own when the wheel starts turning. I don't know about you, but I would be likely to forget to start it fairly often.
My companions on the TA racked up considerable mileage at times while parked in front of a restaurant or store due to a neon sign in the window. It kind of averaged out with the mileage they lost when they forgot to start the computer again, but still it was a problem if you wanted an accurate mileage number. Less of a problem, but still annoying were the momentary glitches under power lines, near electric fences, and other things like that.
Over the years I tried several different wireless bike computers and in every case I either took them back for a refund after some usage or pitched them in the trash. On the other hand every single wired model I used was pretty trouble free.