When is it acceptable to use the first person ("I", "we") in technical reports?
I'm not an expert, but my understanding is that technical reports are generally written in the passive voice. So, unless there's a reason to use first person, I'd avoid it.
That said, I think it's pretty rare that you'd be called upon to write a spontaneous, context-free technical report, so I'm with user1594 in thinking that you need to look at the individual situation. Most large companies and universities will have some form of in-house style sheet that you could consult. Smaller organizations probably have a person to whom you could speak about the issue. Or you could just look up previous examples of technical reports written for that body and see what format was used.
So, if in doubt, I'd go with passive voice, but I'd also try to get rid of the doubt, where possible.
It probably depends on what you mean by a "technical report".
See, one of the first rules about writing is that context is really, really important. So when you ask us if the first person can be used in a technical report, it leads me to wonder who your audience is (just your boss? everyone at the company? the general public?), what the story is behind this question (you must think that first person is a viable option for some reason), and what this technical manual is supposed to accomplish.
In other words, we need you to give us more information.
I'm a technical manager at an advertising agency, so often have to write client-facing documents. Generally, I either refer to my employers' company by name in something as formal as a specification document or in a write-up of a meeting, for example. In something less formal, such as an email, then I would use we where it would not be ambiguous.
Generally, though, I evade the issue by using the company name.