Mid-conversation, seemingly at random, you get the sense that the model has suddenly switched over to 4o-mini (faster generation, stupid responses) without notifying you, and that it has completely forgotten everything that came before in the conversation. In this state, if you explicitly ask it "What was the first message in this conversation?", it will give you the message on which the changeover seemed to happen (or some more recent message), and it will hallucinate about anything that came before, or say something nonsensical like "I can't access a conversation which has ended".
When this happens, if I try to restart a particular conversation by clicking the regenerate button on the first (long) message, it will complain that the message I'm trying to use is too long, even though it worked perfectly fine before. If I try to split up this message into two parts, it will have completely forgotten the first part by the time it reaches the second.
If you try to use o1-preview while ChatGPT is in this state, it will respond instantly with fast generation (similar to 4o mini) and never actually spend any time thinking. (And the responses always seem to begin with "Ah yes! The famous <whatever> problem.", which seems to be a hallmark of 4o-mini)
If you try to generate, analyze images or search the web using 4o, it will either insist that it doesn't have those abilities, or just pretend to do what you're asking of it. (ie, if you upload images, it will pretend that it sees them and just make things up that have nothing to do with the images)
The problem will then just seem to randomly clear up after a few hours. Clearing site data, trying it on different computers, incognito windows, etc. has no effect. Problem doesn't seem to be affecting the iOS app when I try that.
I have ChatGPT Plus, and as far as I'm aware I'm not under any usage limits when this behavior starts (and things work fine in the app in any case).