Napleton's Des Plaines Chrysler offered 3500 for trade of my car signed contract then said they made a mistake told me to bring my new car back des plaines, Illinois

You didn't make it clear as to if you actually kept the car.  If you did, you may have some more problems...big problems...down the road.

Many of the Mustangs (and other Ford cars) use a two piece spark plug.  I don't know if that design was used in 2007, you better hope it wasn't!  This two piece spark plug has a tendancy to break off during removal...it doesn't matter how the experienced the mechanic is...the break off and they break off regularly.  (Research this on the net.)  If any pieces should fall into the cylinder, forget about any long life for that engine.  If it was me, I would NEVER buy a used Ford which has used the two piece spark plug design, period.  If I bought one brand new, the first week I'd have them replaced with an aftermarket one piece replacement.

But there's STILL more.  Napleton is well known as one of the sleaziest of car dealership chains in existence.  Check your paperwork and I'll bet you will find at least one BOGUS, ADD-ON, Phoney fee for hundreds of dollars and/or hundreds of dollars for title work!  The bogus fee will be called "administrative fee", "handling fee", "dealer fee" or other such nonsense.  Its nothing more than a Napleton con-game.  Bogus Billy Heard was sued for millions regarding FRAUD and DECEPTION.  That slimeball closed his dealerships because he knew the regulators had him. 

Many of those same tactics of FRAUD and DECEPTION are practiced everyday at Napleton dealerships as well as others, like all the Rick Hendrick stores.  Napleton, Hendricks and many others are nothing more than sleazy, slimeball, pondscum.  Their SMELL is so bad they are fumigated hourly.  There is no doubt in my mind this experience was one of them playing some type of CONGAME with you.  Napleton is KNOWN for their deception and fraud.

The 7 idiots who voted No on Ramjet's comment must - yes, I'm gonna say it even though I've railed about others doing this - WORK FOR THE DEALERSHIP! There, I said it and I meant it.

Yes, a dealer can pull this kind of crappola on "pre financing", where they let you drive off the lot as though it's a done deal, only to later call you back in because the financing wasn't actually approved.

BUT, if they signed the dotted line giving you whatever for the trade, tell them to go insert projectiles into their bodily waste exits.

 Now that is a word I would use for Team Rebutt. Have a nice day

If you indeed do have a completely signed binding contract that includes the new car and the trade in, tell them to go pound salt.

Is the financing all approved and in place too?
They can't back out of a legal contract any more than you can.