What firmware version on your ObserverIP, and which version on MeteoBrdige?
Note that the "spike" values are equal to the values expected without the spike, but then subjected to the formula for conversion from C to F. For example expected temp at first spike is 76.7F, converted to 9*76.7/5+32= 170.6, and the recorded value is 170.2 (which corresponds to a temp of 5*(170.2 - 32)/9 = 76.77.
So, at spike times, MB applies the conversion for C>F even though it should not. I am going to make an educated guess that you do not see the problem on wunderground or ambient weather is because you upload to those directly from the ObserverIP.
When MB reads data from ObserverIP it reads the value from the Live Data page, and reads the units in use from the "Station Settings" page. If, for some reason, it gets confused about the units being C rather then F, it will apply this unwanted formula. One way this can happen is if you change the units for the ObserverIP from F to C, the MB sees the new units right away, but the Live Data page on the ObserverIP lags behind, making it possible for the MB to see F values with C units, thus applying the conversion (when you don't want it to). This scenario has been reported to Ambient and Fine Offset.
Even if you are uploading to wunderground or ambient through the MB they might not see it because they "sample" your uploads every 5 minutes. If the peak does not coincide with the exact sample they take, they won't see it.
I doubt, however, this is what is happening based on the timing of your spikes. Knowing your firmware versions may help figure this out.