I tried it, and it is nearly fixed.
A view days ago, I had to measure power consumption from a data logger and used this opportunity to play with the Mooshimeter.
All works fine, except when you set the sampling rate to 8000Hz. Then you will still find spikes. Same is, when you use thermocouples.
It looks like the root cause for this effect is independent from the actual measurement.
I uploaded you an ok and a nok SS.
In the measurement I did, was only one LED as load connected. I also crosschecked with a scope, and there were no spikes on the power supply.
Also it does not make much sense, that a LED jumps from +30 mA to a negative current.
You can download the SSs here:https://icsulrich.com:5001/sharing/9KV8gGiK6
By the way, my Nexus 9 tablet updated today to Android 7 and the Mooshimeter APP works without any incident.