I think you have extensive experience with condition inspections. I don’t know if you do annuals.
Well, as of today, I've done about 171 (about) CI's, and zero "annuals". I don't work on TC'd aircraft - only E-AB and E-R&D.
I have not yet done a condition inspection, only annual inspections. So I may do a condition inspection in the future and want to learn more about condition inspection procedure from both an owner and a mechanics perspective. Which is the topic asked in post one.
Gotcha.
So
@Dana has stated that:
The difference is that when an IA signs off an annual with a list of discrepancies, the annual is "good" once the discrepancies have been addressed, and the IA doesn't have to see it again. The required condition inspection for experimentals doesn't allow that; at the conclusion of the inspection the aircraft is either "in a condition for safe operation" and it gets signed off as such or it isn't. If there are discrepancies the person doing the condition inspection can only sign off the CI after the discrepancies are fixed.
And you've asked for FAA references for the inability of the A&P to do that. I assume, but don't know, that if discrepancies are listed as being required to be fixed prior to the Annual being in effect, that someone legally allowed to perform the fixing must sign the logbooks prior to the next flight, saying that the discrepancies have been fixed. That person might be an IA, an A&P, or the owner, if the discrepancy is of a low enough level that it's legal for the owner to do the work.
My position is that whether there is FAA documentation (which there isn't) that addresses this specific question or not, it's a logical impossibility to state, in the logbook, that the aircraft "is in a condition for safe operation", if there's any discrepancy/issue that prevent that statement from being true. I suppose that in theory, an A&P could provide a signoff in the logs as well as a list of things to fix prior to the next flight, and that the plane wouldn't be legal unless the discrepancies were signed off. But since it's legal for your grandmother's dog to work on E-AB aircraft (although an A&P is required for E-R&D), it's unlikely that any A&P (me included) would be willing to leave themselves open to that sort of situation - not requiring proof of remediation prior to providing the signoff.
As I said earlier, if there are safety discrepancies, I just won't provide a signoff until their fixed, and I don't know why anyone would. The fix can be demonstrated in a number of ways or performed by any number of folks (whom I'd need to trust).
@Toobuilder 's comments about latitude and subjectivity is spot on. I've seen signoffs of things that I assumed would have killed the pilot almost immediately, and I've seen A&P's reject stuff that I know to be perfectly safe and acceptable over a million hours of canard composite flight time.
I did a search of Code of Federal Regulations for ”condition inspection”. Nothing listed.
That's because the only place it's referenced is in the aircraft's Operating Limitations. Read Paragraph 23 again, or look through Order 8130.2J for the relevant OL paragraphs for E-AB aircraft.
If you're asked to perform a CI and agree to do so (and if you've been an A&P for a long time and know the build technology of the aircraft you're being asked to inspect, there's exactly zero reason for you not to do it), you'll have all the rope you want to hang yourself and your customer

. YOU will get to decide whether you like something or not; whether you want to make the owner fix a thing or not; and whether you're willing to let someone else fix a thing either before or after you put your signature in their logbook or not. Now, hopefully, you'll review as much information and documentation about the plane in question as is available so that you're going in with SOME amount of education and what to look for. Rattling around in my head is pretty much every modification and fix that's been done to canard composite aircraft; why, and whether or not they're "mandatory". I DON'T have that info for RV's, but all the RV plans changes are on-line, so I review them all and include them all in my inspection checklist, so I know what I'm looking for. I'd hope that all A&P's do the same...
I don't think there's as much definition of what to do and how, and what not to do and how, as you're expecting or looking for

. Maybe that's a good thing, and maybe that's a bad thing, but I think that's what we're all saying here.
Hope this helps.