If you've rooted your Nexus 4 (and managed to get your hands on one!), then a substantial increase in video recording quality is but a tweaked XML file away. As long as you don't mind delving into the file system of your device, here are the steps you need to follow to take advantage of the boost.
Last week, user mohit1234 on the xda-developers forums came up with this easy tweak to greatly boost the video recording quality on the Nexus 4. It involves opening up an XML file on the device and upping the bitrate of the video codec (in this case, H.264). By default, it's set to 12,000Kb/s, but mohit1234 was able to set it to 20,000Kb/s without any ill effects. Note that your Nexus 4 will need to be rooted in order to make this change.
Using Root Explorer or File Explorer, browse to the "/system/etc" folder and locate a file called "media_profiles.xml". Crack it open until you find the section starting with
<EncoderProfile quality="1080p" fileFormat="mp4" duration="30">. It should look like this (courtesy of xda-developers):
Change the "bitRate" setting under "Video codec" to "20000000", save the file and then reboot.
Both the front and rear cameras can be tweaked in this manner, with the
<CamcorderProfiles cameraId="0"> section controlling the former and
<CamcorderProfiles cameraId="1"> the latter.
The xda-developers post includes flashable ZIPs for the stock and altered settings, should you require them.
As long as you don't mind larger video files — understandable as the data rate has been increased by ~70% — there's really no downside to this tweak.