A very large impact on your credit score is the number of account that are currently in collection. Collections accounts refers to the weird stage in an account between a delinquency and a chargeoff. The lending institution at this stage will usually allow the borrower to keep the account open and continue to use it. For example, if you miss 1-2 payments on your house, they will not place a foreclosure on the house right away. Similarly, missing a payment or two on your vehicle will not amount in immediate repossession. It will, however, cause the companies to levy large late fees and move to collect the payments that they were owed.
Getting an account out of a current collections is a large impact on a score. It will not completely remedy the negative impact the account will have on your bureau and score though. The account will still be seen as having been a "collections account" at one point. Lenders can look at the worst-status of any account on file and will be able to see that the account was in collections at one point. They will look slightly better on the account, though, if it is current even if it was negative at one point.
Lenders have been known to remove reporting of negative marks off of bureaus in rare circumstances. A call to the company after the account has been made current may incite the company to remove the negative reporting from the bureau. This is rare, however, and you do not have much leverage for many accounts. Credit cards are more likely to do it since they are open account and are looking to have the customer continue to spend going into the future (so they have more skin in keeping you happy than loans like student loans/auto loans). They are more likely to grant this if it was a one-time occurrence and was quickly remedied. If you are a long-time great customer for them, one small slip up may be seen as a slipup and not a sign of things to come.