I think there are shadchanim who specifically deal with people who have issues. Obviously, a lot of seichel and caution has to be used in figuring out what issues go with which other issues. It may not make sense to set up someone who suffers from depression with someone else who does, but let’s say the girl suffers from depression and the boy is emotionally very healthy but has other issues that are making shidduchim difficult for him, he may be willing to marry this girl. I knew a shidduch like that that worked very well.
Of course, there are some people whose problems render them unfit for marriage altogether, so if someone knows that, they shouldn’t set them up.
It seems (as per the halachos quoted above) that the shadchan is halachically obligated to use caution and not suggest a shidduch if he has a real reason to believe that it will be harmful to one of the parties.