But score isn't everything, score is only half of your credit qualifying. The other half is what is on your credit, such as perhaps the judgments and tax liens you mentioned. What is on your credit is just as important as the scores, as if there are recent delinquent items or late payments even with a high credit score it could still mean you can't get qualified. It's a "What have you done for me lately?" type of approach - they want to see that "lately" (as in the last 12-24 months) that you 'have done your creditors right" by making all agreed payments within the time they were due. Certain situations that can be explained are OK, such as situations arising from extenuating circumstance (medical situation, death of a wage earner, etc.), but anything that was due to just plain old financial mismanagement (forgot to pay the bill, mail didn't arrive on time, etc.) usually needs to be 12 months out, and if there are repeat patterns, even up to 24 months.
Tax liens and judgments are severe, not as severe as a bankruptcy or foreclosure, but more severe than charge-offs & collections - the reason being is that judgments & tax liens can affect a lender's lien position on the home as judgments & tax liens can attach themselves to a title of a home.
For the most part judgments & tax liens need to be paid in full either prior to the mortgage application, prior to the closing on the loan, or at closing on the loan (each lender has different guidelines - be sure to disclose your info/ask questions about their guidelines upfront).... however if you are on a repayment plan, with all payments made on time (typically need to be on a payment plan for 12 months, just starting it yesterday isn't going to cut it), then there are lenders (including us) that will not require the debt to be paid off, but we will include the payment on the debt in your debt to income ratio (pretty logical I'm sure you'd agree).
That also goes for collections & charge-offs too (if anyone reading wanting to know). However collections & charge-offs aren't always required to be paid, it is up to the lender's guidelines and the underwriter's discretion (FHA & VA do not require payoff of collections & charge-offs for approval, so any required payoff of those is always a lender overlay/requirement).
Feel free to ask further questions.