Voltmeter with an OLED indicator

[david]

These displays use a 3.3V regulator which will simply saturate if you feed it with 3.3V and generally they will run down to 3.0V without a problem.  While they will run happily on a 5V supply due to the regulator there is a problem if the micro feeding it is running off 5V.  The drive from the micro to the display will tend to overdrive things but the real issue is the 3.3V ACK signal from display back to a 5V micro.  If using the micro's hardware SSP, the display's ACK signal falls just short of the IIC standard and the display may have broken characters or characters that haven't cleared.  The displays do have pull-up resistors added but they are fairly high in value (10k) but I have never had a problem with them on a low capacitance bus.  You could try adding a pull-up from the SDA line to 5V line (or 4.2V in your case).  This generally overcomes the ACK signal problem at the risk of wishboning the display silicon.
I have also found the regulator on many of these OLED modules rather noisy and on some brands you will see that C2 is missing.  This is the capacitor across the output of the regulator (stability pole).  Adding a 1uF MLCC will fix this.  The regulator devices are multi-sourced and it's possible one brand proved totally stable without the capacitor.
The useful range of a single LI Ion cell like a 18650 or 21700 is 4.2V down to 3.2V after which it tends to fall off rather steeply.  The display is fine over this range but the logic levels can be an issue.

Cheers,
David

[david]

Also note the pin out of the displays changes with brand and even between the 0.96" and the 1.3" sizes.  My photo shows Vdd and Gnd reversed when compared to the earlier front photo.