This is where technology comes in handy. Videos and other recordings don't lie--they give us a chance to hear or see ourselves the way an outsider does. Make frequent recordings of your playing, including your performances, whenever possible. While I usually listen to practice recordings right away, if you have a particularly emotional intense performance (an important recital, etc.), it might be better to wait a few days, then listen. That way you have enough emotional distance to listen more objectively. Likewise, I think it's a good idea to think about listening for specific details as opposed to judging your overall performance with broad generalizations, like "good" or "bad." Instead, ask yourself questions like, are there sections where my rhythm is uneven, and if so, where are they? Don't just think, "that's out of tune!" Ask yourself specifically what notes are out of tune, and are they sharp or flat, and think about what you could do to improve them. Which brings me to...
2. Use Your Tuner and Metronome!
I like to tell my students that we can debate many things in music, from Historically Informed Performance Practices to subtle interpretations of phrasing and articulation. But some things are fairly objective, and those things include rhythm and intonation (for the most part--I know there's fierce debates about equal vs. meantone temperament, but let's set that aside for the moment). The metronome and the tuner will not lie to you, but give you a fairly accurate assessment of your playing. That's valuable information that we all need!
3. Audience Feedback
Even a non-musician knows when something sounds wrong or boring. Yes, some pieces aren't for everyone and some modern music has lots of dissonance that's meant to sound "wrong." But if an audience doesn't seem interested or actively dislikes what you're doing, then you have a problem, even if the problem is choosing the wrong repertoire for that particular crowd. If the audience feedback is vague or you're not sure what they don't like, hopefully you have a video or a recording you can use to try to identify the problem yourself.
Facing our mistakes and weaknesses is one of the hardest things that we have to do as musicians, but if we want to improve, it's one of the most necessary.