There are various misconceptions here.
The emitter resistor value has no effect on efficiency. All the current for each LED is coming from the 5V supply. Whatever part of that voltage the LED doesn't use times the current is going to be wasted as heat. Small emitter resistors only more the dissipation to the transistors. The total dissipation is the same.
I thought I mentioned it in your other question, but the emitter resistors should be a larger value. At 1 Ohm just 1 1mV offset will cause 1mA thru the LED, which is probably dim but visible. From your voltage divider ratio and the 1 Ohm emitter resistors, it looks like you're aiming at a bit over 300mA LED current. Didn't I go thru a detailed calculation of the emitter resistor value in your other question?
I don't know what kind of LEDs these are, but most likely you can afford at least a volt accross the emitter resistor, so 3.3 Ohms would be a better choice that will give you more control.
As for the not quite 0 and 5 volt output, that's probably something the Arduino is doing. Keep in mind that arduinos are Simplified for the masses. It wouldn't surprise me if there is a resistor in series with each output as protection.
The opamps are probably working fine enough. Every opamp has some offset error, and if these are a little positive, their outputs will go high just enough to turn the transistors on a little to make that offset voltage appear accross the emitter resistor. This is yet another reason for using a larger emitter resistor.
Yes, it sounds like you are seeing artifacts of toothbrush frequency vibrating your head and therefore your eyes, and that beating against the LED refresh frequency.
This is a similar effect to eating potato chips (actually anything crunchy) while watching the LED display. In that case the head vibrations are more random, so parts of the LED display will appear to jump around randomly. Some segments will be displayed during a head-high part of a vibration, and others during head-low. These will appear in different locations.
LEDs are refreshed all kinds of ways. A lot has to do with how clever or competent the engineer was that wrote the firmware. I've seen naive refresh algorithms that simply do each digit in order. Those have the most apparent flicker for any one refresh rate. Better means interleave digits, sortof like interlacing of old TV scans lines. The whole display is still refreshed at the same rate, but the apparent flicker is at least in part related to the interlace rate. There are fancy schemes which interleave both digits and segments, but these are often not possible with common displays where whole digits are already partially wired together.
Best Answer
The properties of aging on transparent substrate LEDs have been documented in research by many but are not handy to me the time of this writing. I have known this for about 10 yrs so Google or Microsoft Scholar ought to have some papers on this. I got mine from EOS by NDA.
Generally 10% of rated max current is needed to prevent some corrosion of the crystal electrode interface. But then with 50kh given as expected min MTBF this has been greatly improved by many brand name suppliers by quality controls to millions of hours if you want to use PWM dimming to 1% some of the time, that would be OK if 100% of the time was also experienced.
Heat generally has a positive aging effect initially only either by soldering or operating at rate temp for several hours or days. This can burn off leakage R and sometimes crystalline-metallic shorts. (dendrites)