If you have a solid self assessment of what you know, you can consider when information is supported by what you know. For the parts that aren't, you consider how critical they are, and identify the area that needs a deeper dive, where you either link it back to other areas you have confidence in your own knowledge or work to expand your own knowledge (using other resources). Then cross check knowledge. The cheap way you can do easily is to cross check between AIs/harnesses, because hallucinations happen randomly, so two different models in two different harnesses having the same hallucination is extremely rare. The more expensive option, which should be used when the information really matters, is building your own knowledge. Have the AI help guide you to resources, but not be the resource. While using non-AI resources, check you knowledge against them and the AI. Test yourself with classical resources where it really matters.

Part of it is using good judgment. Is the AI's claim reasonable if it came from another person? If some random person gave you a 2 page paper proving P=NP, would you even spend time to look at it, or would you simply toss it without caring to understand what error they made. Much like how scientists (and even the patent office) simply refuse to entertain any perpetual motion machines. Maybe if an expert in the field proposed it, and even that would depend upon how ("Hey, I found a source of free energy!" vs "Hey, I'm working through these equations and the energy term isn't balancing, can you help me find what energy source I'm missing?").

This does pose a problem. Those who are the best at understanding the limits of their knowledge and at teaching themselves need the AI's help the least but are in the position to be able to use AI with the best chance of not being misled. Those who lack these skills and would benefit the most from a personal educator, thus receving the biggest benefit in theory, are the ones most likely to fall victim to the errors made by the AI.