Will a bad plug receptable cause other switches to stop working?

It could! If wired in series in a way that is commonly done, linking receptacles on a common circuit, this especially true with GFCI outlets, allowing one GFCI to protect all outlets down stream. However, it would be unusual to find another type of device wired in this way.

Regular receptacles have two screws on each side for the hot and neutral wires. A daisy chain of sorts is created when both blacks from two romex cables are connected to the two screws, and this continues down the wall to the next receptacle. Some problem with the receptacle or the wiring could cause a loss of power (or neutral) down the line. One that is obscure to the novice is the break -off tab near the screws. This is used when there is a switch controlling one of the out lets and the other is available as a standard outlet. If such an altered outlet is being reused, or one that some how was broken off, the two screws are no longer connected, and will not make the daisy chain as planned.

It is common practice that circuit is provided to an area in new construction, and by code only seven or sometimes eight devices are allowed to be connected. Most often this a room light, some receptacles in that room and possibly receptacles in a wall common to another room. Depending on the routing of the "home run"...the wire from the breaker and the distribution panel... this could be any junction box that is part of this circuit. Problems here can affect any other part! Considering the possibilities of remodeling, upgrading to ceiling fan ...it is hard to tell. If necessary you may have to figure out witch box has the "home run" feed, disconnecting all there and reconstructing the circuits until the problem is isolated.