I made a small mistake in my profile. Should I fix it? Can it get me refused?

Yes, fix it. Always. While you're still in the pool, you can update your profile at any time. If you've already submitted your application, use IRCC's webform to correct the error and explain it. Small honest errors (a typo in a date, a wrong postal code) rarely cause refusal when corrected openly. Problems begin when a mistake changes your points or eligibility and goes unmentioned: that can look like misrepresentation. Transparency protects you.