So, I have had experience with a decent looking company. I flunked their test due to poor explanation and very open-ended expectations. They had two parts, which was a coding section and the other was a find all the problems in this file. This was all in C, so it was painful as there are A LOT more mistakes that can be made and to be frank, I didn't know what all to look out for. They said both section should take only 2 hours in total, but you have unlimited time.
Failed the coding section, due to not understanding the problem well enough. There were a lot of issues with the explanation and it wasn't something that could simply be explained away. I had some errors in it, but no where near as big as the misunderstanding due to the poor examples and explanation.
Failed the analysis section, due to not finding all the errors they were looking for. A lot of the errors you'd have to be scanning this file like a hawk for and my theory was that going that far down was unnecessary if they were intending for you to finish that and the coding in 2 hours.
I got back to them and told them what I thought about it all, as kindly as I could. I had the realization after that about not wanting to use C because of how easy it is to shoot yourself in the foot and it will flatout let you do it. I explained that I misunderstood the problem and how it was supposed to work. Even put unit tests at the bottom of the file to test everything.
My advice is it's a good idea to give advice, just don't expect that it's going to change their decision. I considered it very kind of them to give me feedback, as it helps me get better at the risk of revealing more about the contents of their hiring test. So, I'd say if they had issues in it, then it'd be good to point them out but don't look at it as a chance to get yourself hired. Look at it as returning the favor for giving you feedback, which can be very rare nowadays. Besides, assuming everything you said is true, if they did that bad of a job of checking their content and aren't willing to admit their failure, then do you really want to work for them in the near future?
I'd let your recruiter know the problems as well, but you may not hear back from them for a while anyways. I've heard, but have not verified, that when applicants fail to get a job under a recruiter that they sorta ghost them about opportunities for a while as they believe that they won't get the next job either that they put the time and effort in to get them an interview for. They are paid only if you get the job, so it's just kinda the way it is. Not to mention, recruiters know the technical side at a very basic level, if at all, so they aren't likely to be able to understand the topic well enough to know what happened.