Don't hesitate to apply for a loan and go house-hunting just because you were late on the car payment last year and think you won't qualify. You may not get the best available rate, but you'll probably still be able to get into the house. This is why the credit report is one of the first things that is addressed in the loan process. It does no good for you and the loan officer to agree on a rate and fee structure if, after the conversation, the credit report indicates that you won't be accepted by the lender offering that rate. Whether fee or free, it's good sense to order one occasionally just to see what's there.
Creditors make mistakes and agencies make mistakes.
If you can prove a late payment is unjustified, it usually just takes a call to the creditor and they send a letter to the agencies asking them to remove the mark. Also make sure to get something from the creditor addressed to you saying the same. In addition, you're less likely to have another surprise on you're hands. You'll just be eliminating one more possible surprise. Remember, the underwriter will take the credit report as being handed down from the mountain unless you prove something different.