I have installed new recepticals all around the house but I have one receptical in the master bedroom with an open neutral and two with open grounds per a grt-500 circuit tester. The two open grounds are still functional but the open neutral is not. I have checked all of the wires and they are tight and all of the hots are on brass and the commons on silver. I have checked all of the ground wires and they are secured to the back of the box. I have hot at all of the recepticals. The only caveat to this is I installed a remote ceiling fan. One day the fan, by itself changed direction and went the opposite way. I also smelled wires getting hot when this happened. After I installed the fan the light switch on the wall failed to work. I am at my wits end if someone can give me a hand that would be awesome.

Each cable will need to be traced, relating to the fan. There must be splicing , not necessarily in a junction box, with very poor connections. This can be in any ceiling outlet, or switch box. Even worse, can be buried splices.

If the home is older or has had many remodels, these are prime real estate for hidden gems.

There is a shared neutral most likely the cause of this. Are there any 3 wire cables, two separate circuits with black, red, white wires? These are shared neutrals, and a break in the white can cause voltages in each of the black and red to run very high.

Fix this right away, the high voltage will damage everything it hits.

I would check recepticles on each side and verify secure. If switch near there, could be connection there. It will be on that circuit, maybe go to panel, if comfortable and able to safely work there, check if that circuit breaker for that room, goes out of panel in same cable or conduit, follow back to breaker and see what circuit may be sharing neutral.
It could be another bed or bath or anything, it will help narrow down to those 2 circuits.
Check the neutrals and that fan connection. Eleminate the remote or replace if defective.
Going backwards is not a sign of being bad.

The fan what type of wall switch is it on? Does it have pullchains?

Sounds like the receiver inside the fan burned up, rather than a problem with wiring.

Ceiling fan remote controls - help and FAQ- Ceiling Fans N More (http://www.ceiling-fans-n-more.com/ceiling-fan-remote-controls.php)