You can start law school with bad credit. And pass the charcter and fitness test. If you have a judgement, you have to pay it and any outstanding bills to the government like tax liens or parking tickets. For the other bills, make some type of payment on a contineous basis for like 6 months to a year before you take the bar exam. You can tell the committee that you are making a honest commitment to paying your bills. Also you can send a letter to the credit agencies that can be attached to your credit report. In this letter, you can discuss any hardships such as illness, etc that has made it difficult for you to pay your bills. That way, anyone who pulls your credit report can read the letter and know that you have fallen on hard times.
You can't just fix your credit before law school. They update credit slowly like on a 6 month basis. And you have to balance it with good credit like secured credit cards, etc. Just plan to get some control over your credit before you take the bar. If you do well your first year, then you have a chance to get great summer jobs that pay well. One of the firms I prebid on for OCI has a salary that will allow me to cut down on a few bills with just 2 1/2 months of work.
Also like Schwing said, know what your state bar association wants. Some states like Florida are harsh on bankruptcy and other things. Other states like CA want you to pay any outstanding judgements and bills to state or county agencies and make an attempt to pay off your credit. As long as you haven't applied for bankruptcy you should be okay.
Like vixierat stated, as long as you're actively working on your credit, you will be fine. Also keep any documents or canceled checks that you have sent to bill collectors. They are notiously slow with reporting payment to credit bureaus so have your paperwork showing that the bill has been paid. Also request in writing from the bill collectors that if you pay the debt in full that they will report it positive to the credit agency. Make sure you have documents to cover yourself. Good luck.