It seems that Samsung has broken Bluetooth tethering on their latest Galaxy Gear update for the Galaxy Note III, even when using the null_ ROM. But I have a solution. Are you having issues with extremely slow downloads and multiple time outs. Does it take ages to download from the Play store, or can't you download from the Play store at all? Read on.
I installed the latest update a few days ago, and today I needed to install some additional software on the Galaxy Gear. I simply could not get the Play store to work. It loaded and loaded, but never got anywhere. One single time I got it to start downloading, but after a half an hour the download of 2 MB was still at 3%. I tried absolutely everything, but could not get it working. I tried disconnecting my Bluetooth keyboard and mouse, thinking that they somehow were saturating the Bluetooth link. I tried connecting to multiple other phones and computers. I tried rebooting everything, multiple times. I tried clearing settings. I tried disconnecting and re-pairing devices. I even tried updating to the latest version of the null_ ROM. But no matter what I did, the issue prevailed. I googled for hours, with no solution found. However, I saw a lot of people complaining about this exact problem. I also so a lot of people answering that "Well, Bluetooth tethering is slow. This is ordinary." which, pardon my French, is complete BS. Yes Bluetooth tethering is slower than WIFI, but it is not that slow. You aren't exactly able do to HD-streaming, but downloading from the Play store, and surfing the web works quite fine (like it used to do before the last Galaxy Gear software update from Samsung. This kind of bad performance is quite obviously due to something being broken, and anybody who says different is not telling you the truth.
I was about to give up, when I finally stumbled upon a solution. First I paired my Galaxy Gear with my Samsung Galaxy S4 which does not have Samsung Galaxy Gear software installed on it. Next I turned off Bluetooth on my Galaxy Note III to ensure that the Galaxy Gear disconnected from it. Finally I activated Bluetooth tethering on my S4 and on the Galaxy Gear. Suddenly, working Bluetooth tethering with even better speeds than I was experiencing on the Note III prior to the latest Samsung Galaxy Gear software update. So there you have it. To get Bluetooth tethering working on the Galaxy Gear running the null_ ROM, you have to disconnect it from all devices running Samsung Galaxy Gear software, pair it with a device not running said software, and activate Bluetooth tethering.
I'm really hoping this wasn't intentionally done by Samsung, but I find it very strange that this feature, that worked fine when using previous versions of their software suddenly stopped working. Specially considering how much effort they have put down in only allowing authorized applications to use the Bluetooth link when running their stock firmware.