when I remove the first / i instead get the following error:
[Mon Jul 14 07:37:58 2014] [error] [client 192.168.1.78] Invalid URI in request GET ~Peder/wifi-weather-station/sensor.php?temp=25 HTTP/1.0
and I haven't been able to find any information regarding invalid URI that brings me further towards a solution.
The file location is probably not correct. Use the local directory path, not the Apache path.
edit: I did not notice the leading double quote is not correct until I posted line 7 here. Do you notice it is different than the trailing double quote? They should look the same.
You did not post the entire Apache access log, but I will presume the status code returned was "500 - Internal Server Error".
It turned out to be partly having the right local address (used http://localhost...) and wrong double quotation marks, not quite sue why that was an issue I only used the ones I have but they seemed to come up in italics... so I ended up cutting and pasting the original doubles.
thanks johnwasser and SurferTim for leading me to the answer