Conscripts were divided by Conscripting Commission into several categories, based on physical and mental conditions, according to Military Service Law, enacted by 1939 - see [1]. Law of 1939 removed class restrictions. Previously conscripts from exploiter classes were not allowed to serve. There were other major changes.
Conscripting Commissions operated permanently during WWII in every (район = area ~ county in US) Area's Military Commisariat (РайВоенКомат). In peace time, conscription was done twice a year, spring and fall (and still is).
Fit for regular service without any restrictions (годен к строевой службе без ограничений)/ with some restrictions
Fit for irregular service (годен к нестроевой службе) with/out some restrictions
Fit for auxiliary service (ограниченно годен к вспомогательной службе) with/out some restrictions
Unfit (негоден к службе). Aka белый билет = white ticket - as conclusion about being unfit was printed on white paper. Other categories have colored bands and marks, indicating branch of service.
Each category had subcategories - esp. 'Fit' category was then split into specialties - e.g. all air gunners must have perfect vision, all submarine sailors, tank drivers must be healthy, but of short height, airborne troops required most physically fit, preferably with some sport achievements etc.
Color-blindness won't make one unfit - regular infantry units were taking them.
Missing an eye or a limb? Still might be fit with restrictions - many wounded and recovered were conscripted later, but usually those were volunteers, who insisted.
Irregulars - like logistics and services away from frontlines, watchmen of military stores etc. Some have minor health issues, a lot were older men in 30s and 40s.
In 1942 and 43 many criteria for unfitness were relaxed, so more previously unfit could be conscripted.
OK, and now short list of what would make one unfit :
blind, deaf, mute persons were unfit
serious heart conditions, like congenital heart defects
serious infectious diseases - but such dangerous and debilitating disease as trachoma at early stages will lead just to forceful treatment.
any history of mental illness
criminal record (with caveat - there were special opportunities to volunteer)
having a flat foot means unfit
That's health reasons. Other reason was value of individual to the country at work. Workers at important factories (esp. military-related) were often freed from conscription (so-called бронь = armor). Still, many of those chose to volunteer to Divisions of People's Militia (ДНО - Дивизии Народного Ополчения) or just begging local RaiVoenKom to conscript them till they gave up and send them to front.
There were, of course, individuals who did not wish to serve and they were chasing white ticket with great efforts - even going as far as mutilating themselves, simulating tuberculosis (or even contracting it) etc. All confirmed draft dodgers were prosecuted severely - and punishment was often a place in ShtrafBat = disciplinary battalion.
In general, many determined dodgers were able to avoid frontlines, sitting out the war in Moscow and other large cities. They weren't popular though.
Sources
Law of USSR about universal military service, 1939, edition of June 26, 1941. This edition was in effect during WWII.
Scanned Conscript's Map = Призывная Карта, 1941. If you page thru it, you'll see a lot of data and sign-offs from specialty doctors.
Order of NKO N 336, 1942. It had the расписание болезней = schedule of diseases in appendices and instructions to medical personnel how to classify conscripts. Long and complicated. Sadly, it's not posted anywhere and way too byzantine to attempt direct citations. Here is current расписание болезней = schedule of diseases of Russian Army - didn't change that much from WW2, just more reasons for unfitness added and some eliminated diseases dropped.
Order about correcting deviations from giving citizens "armor" and delays from conscription = приказ об устранении нарушений порядка предоставления гражданам брони и отсрочек от призыва, № 147, 1942 . Very interesting document, describing several instances of draft dodging.