Based on the comments to the answer by Dougie, it seems that there may be some confusion / linguistic issues with what's meant by "counterfeit" and therefore disagreement about even basic things like whether or not any exist.
So let's break things down into a few cases:
- If you're concerned that someone is making clone processors, that's probably not happening for the reasons that Dougie indicated.
- If you're concerned that someone is making boards that look like Raspberry Pi but have a different processor, that is probably also not happening. Likely there'd be news about that that people here would have seen.
- If you're concerned that someone is selling boards with authentic Raspberry Pi parts that have been used or mishandled in some way, it seems likely that has happened somewhere in the world, although I'm not aware it's a big problem. (Someone, somewhere, has almost surely soldered something to directly to a Pi, decided to undo it, and stuck the now-used Pi back in the box to be distributed as new. Just as one possible example.)
- If you're concerned that someone is selling boards with some fake parts and some authentic parts, I think that's probably also happening, but, again, I've not heard of it happening on a large scale.
Seems like Dougie is only including the first and maybe the second above as "counterfeit", whereas it's more common (at least in US-based industry - maybe other countries have different standards or different words in use for the various cases) to call any of the above "counterfeit". If any part on the device has been changed or modified after it left the OEM, then the whole Pi is "counterfeit" if sold as new even though some components in the Pi - like the processor - may be authentic. (In the latter two cases, if you mark that same used / reworked Pi as used / reworked, it's no longer counterfeit. It's just used / reworked.)
(I was going to provide a link to the US Commerce Report "Defense Industrial Base Assessment: Counterfeit Electronics" as a reference, but it seems to be gone from the web. If that comes back later and you really want to see it, you'll have to search.)
Getting to your question of what to look for:
- The processor and various critical components should have markings similar to those shown on the raspberrypi.org webpage for the product that you bought. ("Blacktopping" - where markings are faked - is possible, but unlikely for the main components ala the first two cases above.)
- The board itself should also be marked pretty consistently with the images on the webpage. No spelling errors.
- The board and components should look factory-new. By that I mean there shouldn't be signs of stray solder, scratches on the green solder mask, etc. that suggest that parts have been moved or replaced.
Once running, you should also be able to use all of the supported software, e.g. Raspian, directly.