I hope noone's taking what I said wrongly. I do not wish to correct someone just for the sake of pointing out their mistakes and I don't act as if I know everything. My techniques obviously will have mistakes but I have the sensei and sempais to correct me. If I am having problems, someone is always there to help me.
All you need to do is worry more about your technique. If the instructor is around to correct you then they are around to help your partner. It never dawned on me in my early days of aikido to want to correct someone or to at least worry they are making errors, too. I was still too busy figuring out where my hands and feet went as nage and as uke still figuring out how the heck to do a roll out of a particular technique.
I guess you guys must be wondering 'what would a beginner like me know about Aikido?'. I admit I know very little at this point. What mistakes I've seen in others are usually the ones that I've done before and have been corrected. Anyway, I'm too shy(always have been) to say anything so no worries there.
Actually, that is what I think when a beginner tries to correct me. Here's a better example other than the excessive corrector I previous described. The instructor demonstrates a technique: yokomenuchi gokyo omote with an irimi opening. I did a tenshin opening instead, but had a mind fart and didn't do the irimi although I had the full intent to do irimi not tenshin. I reverted to what I had been ingraining into my mind for my 2nd kyu test. However, newbie/ beginner says "you did it wrong." I think to myself, "ergh, I just did something else, but say, "thanks for pointing that out." I continue doing irimi opening instead of tenshin. I then just let him do what he thinks is right when it's his turn. He then did tenshin, too, btw. I say, "it's a lot harder than it looks." He nods. (He was just getting ready for his 5th kyu test.) Sensei comes over to help.
Now, when I'm working with someone more senior. The first thing that I do is to do my best to give honest ukemi. I go where they lead me and don't necessary go "where I'm supposed to go." For example, if we are doing kaitennage and they don't get my head, I stand back up, but my ukemi is also good enough to take an iriminage when I do that. Most of the time that's the kind of feedback my seniors need. The next time they throw me they have my head.
If I want to say something to a senior, I ask -- do you mind if I suggest something? But remember I'm not a beginner any more, but I'm still not a their level. Usually the senior welcomes it. But then again, I've been training with them for years and they know me as well as I know them, and it usually is an exchange rather than a correction session. But usually, I only do this if I have more of a training relationship with my senior where we have developed this overtime and it's more of a mutual training partnership than a sempai/ kohai kind of thing.
I do have many "mutual training partnerships" with those who are only a year or two behind me. They're my best training partners. We know each others limits, but still can go "all out" with each other if we wanted. From these guys I don't mind the assitance. So you ask why with them and not a newbie with three classes? The answer is simple. I have developed a training relationship with them over the past few years. It evolved out of respect and trust. You can develop that, too. But three classes won't cut it.
Like I said in my other previous example (the excessive corrector) I'm beginning to develop a better training relationship with him. It will happen where you can have a positive exchange with your partners, but yes, you will come across as "you think you know more aikido than your seniors" if you just try to start correcting them on your first few days of practice.
So, what do you do when you see a senior student made a mistake that you were once corrected on? First, don't assume they don't think they made the mistake. Second, continue giving them honest ukemi (the way it's taught in your dojo). Third, just worry about your mistakes and not your partners. Finally, once you get more training time in who knows they might want you to say something, but considering you only have three practice days in, then that's not enough to develop a relationship without insulting them.