RF Feedback is caused by being in close proximity to a source of High Level RF Energy. It doesn't mean that your equipment is really at fault, other than being too darn close! Anything electronic is a potential victim for RF Feedback and it will be quite apparent when RF Feedback is present!
The simplest cure for RF Feedback is the RF Choke. A RF Choke is a coil wrapped around a ferrite core to impede the flow of RF Energy. Radio Shack manufactures a snap on unit, it works well. A cheaper, and sometimes just as effective, alternative is the ferrite rod from an old AM Radio's loopstick antenna. Whatever you can come up with should be used. The key to using RF Chokes is in the amount of turns you can use: The more the better. Places to use chokes are on the AC Power cords and ALL Audio Cables. Electrical tape helps keeps the wraps in place.
Another simple way to reduce the possibility of RF feedback is to make sure that any patch cords or audio cables are high quality shielded cables. Cheap cables are more trouble than they are worth. Also try plugging your transmitter and audio source into different AC outlets.
If you still suffer from RF Feedback problems, the next step is to install Bypass Capacitors into the effected equipment. I suggest using .01 uF Ceramic Disc capacitors rated at 1000 volts. To properly de-RF a piece of gear, you need to concentrate your efforts in two places. First, the Power Supply of the unit. Typically, RF will enter via the AC line cord and get into the power supply affecting everything else. Open the unit, MAKE SURE IT'S UNPLUGGED! Locate the power supply, if you don't know what a power supply looks like you might want to find someone who does. Places to install bypass capacitors are on each side of the AC line cord to ground, across the Secondary windings of the transformer to ground and finally, across the rectifiers to ground. This should clear up any RF getting into the power supply.
Should you still suffer, the next step is to bypass all the line in and out connectors on the gear. Simply connect your capacitor from the Hot Side (Center Conductor) to the chassis ground. Also make sure the equipment is properly grounded in the first place! Do this for all the connectors, regardless if they are used or not. And finally, don't forget about your speaker connections, they might be bypassed as well since speaker wire tends to act as an antenna!
If you try all this and you still have problems, try moving the transmitter or antenna farther away, sometimes a few feet can make all the difference in the world. You may even have to resort to trying another tape deck, some cheap tape decks are impossible to protect from feedback.