What would make a laser measuring device more accurate
-The way how the laser is used is the limiting factor. I list a few ways and their accuracy that I can think of.


Angle of reflection: angle is measured with a line sensor. The location of the peak intensity is proportional to the distance. Accuracy is related to the line sensor pixel size and the algorithm. I have seen accuracy = 100 um sensors with range of 30 to 50 mm, so 0.05% of the distance.
time of flight: Calculate how long does it take for pulse to travel to target and back. Accuracy related to sampling speed and measured distance... 1/8th of an inch requires 5 GHz sampling rate.
interferometry: accuracy is the same order as wavelength of the laser (red 600 nm). This requires some mirrors and steady instrumentation (read: expensive), so not for all applications. 


I think that your tape measure uses time of flight (TOF) measurement. There are specialized TOF chips, so you don't necessary need a fast microprocessor.