Does each photon have a unique wavelength? Since the frequencies (or inversely, wavelengths) of photons are part of a continuous realm, doesn't this mean that no photon has exactly the same frequency?
Two photons might have the same apparent wavelength due to our measurement limitations, but that doesn't mean they'd be exactly the same.  In a continuous realm, how can anything be exactly the same?  Also, there seems to be no uncertainty mechanism that limits the accuracy to which the frequency can be measured, so no help there either.
 A: The uncertainty principle limits our ability to determine the wavelength of a particle with infinite precision. At the same time, there is no fundamental reason why any two photons (even if generated by exactly the same process) should produce exactly the same wavelength; however, you can be sure that there will be plenty that are the same within the limits of nature's ability to measure them (note - not our limits, but those of nature).
Whether that is sufficient to say they are the same - or just "not observably different" is an area of philosophy that I don't feel qualified to enter.
A: Surely you'd agree that all electrons and protons are $exactly$ the same (indistinguishable).
Now consider a regular Hydrogen-1 isotope: A proton and an electron bound together. There's definitely more than just one of these atoms in the observable universe.
Well then consider an electron floating around the $n=2$ shell of a Hydrogen-1 isotope, then falling down to the $n=1$ shell (this event will emit a photon) - I think you'd agree this has probably happened more than just once in the history of the universe.
Every time this has happened, a photon was emitted, with a particular wavelength (determined by some equation). Different experiments might yield different measurements of that photon's wavelength (due to limitations of measurements, like you mentioned). However, according to Quantum Mechanics all the photons emitted through the aforementioned process had exactly the same wavelength.
Maybe there's some (unbeknownst to me) QFT corrections which will alter the wavelengths for different settings in the above scenario, but I think you get what I'm getting at. There are certain processes which occur in the universe that are perfectly reproducible, which will emit photons of the exact same wavelength.
EDIT: As many have pointed out, I completely overlooked broadening of the line widths due to the uncertainty principle, so my example doesn't work at all. 
