I'm seriously considering either switching to half time or taking a Leave of Absence due to some personal problems. I know ERAS asks for delayed graduation reasons... how much would either of these options hurt me while applying for residencies?
A poor performance in medical school is going to hurt you more than delayed graduation. When many of my medical students come to me for counseling, I definitely recommend taking a voluntary leave of absence rather than taking the risk of "failing out" or "extreme drop of grades" because your personal life is beyond your control. If you need a year to get your personal problems under control, take it and get things under control. You are not superman/woman and many times things happen that need your undivided attention.
If you were in an auto collision that caused you to need months of rehab but ultimately you recovered your physical health, would that be held against you? No it would not and having demanding personal problems is not any different. The important thing is to get your life under control so that you can come back and perform your best. It's life and sometimes it happens. The smart thing is to realize that the timing is not going to be what you expected when you started school and stop worrying about it. Ultimately, your future patients will never ask you how long it took for you to graduate.
In terms of the Match, you do need to be sure that you are going to be able to start residency on time within the year that you participate in the Match. If this is not possible, then take that time and do something constructive such as Masters Degree, research, learn Medical Spanish etc and participate in the following year's Match. This would be the case if your graduation was not until December but your residency program started in July. You would not be able to start and most programs won't wait for you to graduate. A better course would be to enter the Match the next year and find something to do between December and July that would be career enhancing.
The situation is what it is and you have to find the best solution that will solve your problems and allow you to graduate as strong as possible. In the end, you do what you have to do to survive. There are plenty of residency programs that won't care as long as you have graduated and as long as you have taken care of your personal needs and are ready to work with undivided attention.