The prosecutor "drops" the criminal charges for a wide variety of reasons. It is the sole discretion of the prosecuting attorney to determine whether enough evidence exists to convict.
Whether or not a case for malicious prosecution exists needs more detail?
They are really hard cases to prove and can be very expensive to litigate.
If the prosecutor had any other reason (to busy, no independent witness, shaky documentation etc...) upon which to base the case being dropped, that will be the defense used in your lawsuit by the person who called the police on you.
Also, dropped charges are not the same as a guilty verdict. It is true no further action is going to happen, but you have not been convicted of the crime alleged if the charge was dropped.
Charges dropped is not a legal term. It is important to know how the charges were dropped. Was there a motion to nolle pros the charges, or did they use the term sol. Each has different legal consequences. Some people say the charges were dropped when they received supervision or probation.