First check the date of any bad credit transaction. If it is older than seven years, the credit bureau has to remove it. The exception is bankruptcy which stays on for 10 years.

Let's say that one of your creditors has put an error on our report. Contact the creditor and ask them to remove the error. When they do so, make sure that they have contacted the credit bureaus. Keep copies of all correspondence. Document phone calls by following up in writing to confirm the substance of the call.

If the credit bureau made the mistake, challenge it. By Federal law, it will have to delete the disputed information if it cannot be confirmed. They sometimes will just remove an item summarily if checking the item is more trouble than it's worth. Both the credit bureau and the creditors have 30 days to resolve any error. In practice, this process can take longer. 

While a note of explanation ("I lost my job, got sick, went through a divorce, etc.) may help explain a rough patch to a loan officer who is evaluating you for a loan, it is a BIG mistake to send such notes to the credit bureaus because those notes may stay in your record longer than the offending transactions which vanish in 7 years. 

After all this effort, you've finally removed the errors. Congrats! There are even more things you can do to increase your credit rating.