I drive a 98 Grand Marquis and my friends and i disconnected my muffler when i first got it. They work on cars and all work at an auto parts store and said that it wouldn''t hurt the car at all. (we just disconnected it to make it sound cool). I had to put it back to get an inspection and one of the mechanics said that if i have it disconnected some valves or something would be damaged? can anyone help me by telling me which of them is right? Will disconnected my muffler harm the engine?

disconnecting the muffler does nothing adverse to the car mechanically (sometimes helps because it may improve exhaust flow). Having a rusted out muffler that causes excess back pressure can cause more problems. They were feeding you a line to try and scare you. the best option would be to put an aftermarket muffler on the car. Something that allows for high flow.

the only issues would be heat on the rear axle and gas tank if you don''t connect the pipes through to the tailpipe. These can tend to be dangerous, which is why it is best to patch exhaust leaks or repair them as soon as possible. it''s mainly the heat that causes problems. Toxic fumes can also be an issue, especially if the break is between the engine and cats (not your case though).

DON'T Disconnect Your Muffler !!
 

NO, removing your muffler will not "damage some valves" or "cause catalytic converter failure", or some such nonsense.
HOWEVER, you MAY die from carbon-monoxide poisoning !!
It is NOT a good idea to just "disconnect" your muffler to make your Merc sound "cool", or for any other reason.

If you can't afford a dual exhaust, your best option is to install a straight-through muffler. I suggest a MagnaFlow glasspack, for lots of reasons:
1. The MagnaFlow glasspack has NO internal baffles or louvers to impede exhaust flow.
2. The MagnaFlow glasspack can be mounted "backwards", as it is non-directional -- flows equally in either direction.
3. The MagnaFlow glasspack is fully ALUMINIZED to prevent rust-out.
4. The Magnaflow glasspack has a straight, perforated tube, with no internal louvers that reduce the internal diameter.
5. The MagnaFlow glasspack has a "stranded rock wool" packing that doesn't burn out and need replacing.
6. The MagnaFlow glasspack is very inexpensive, and delivers the most "bang for the buck" than other "performance" mufflers.
7. The MagnaFlow glasspack delivers top performance at all rpms, unlike those expensive "tuned" mufflers that flow best only at certain rpm levels.
8. The MagnaFlow glasspack has a mellow tone at low rpms, but "talks" nicely when the pedal goes to the metal.
9. They are LEGAL, with sound levels at 82 db at warm idle, and 88 db at open throttle.
10. You WON'T hear anybody yelling "Look at THAT dumb-ass and that noisy old junker!" as you drive on by.

NO, I don't work for or sell MagnaFlow mufflers -- but I run a pair of them on my '95 Grand Marquis Restoration. I'm very satisfied with the sound, performance, and economy.
Photos show dual exhaust: Walker H-pipe; MagnaFlow 2" glasspacks (#18134); Walker Tailpipes; Stainless steel, slant-cut tips.