It should be noted that no on-site inspection was required by SALT I; all verification was performed by “National Technical Means of Verification” (NTM) which is a euphemism for satellite electro-optical imagery and radar tracking of flight tests. The more comprehensive SALT II was never ratified and so no non-NTM verifications were performed, although the US and USSR both ostensibly complied with the provisions of the treaty (which largely resulted in taking obsolescent and maintenance-intensive systems out of operation). On-site inspection was performed as part of START I, but this was starting in the mid-'Nineties, after the dissolution of the Soviet Union when there was essentially no budget to perform missile system maintenance. We know that there reliability issues with some of their systems, but there is no reason to believe that up to the latter Gorbechev era that the USSR was not capable of launching the bulk of its operationally fielded ICBMs, including the vaunted R-36M (NATO reporting name SS-18 ‘Satan’) which in the Mod 4/5 configuration could carry 10 live >500 kT RVs plus decoys (still being used in repurposed form as the Dnper space launch vehicle) and the rail-mobile RT-23 (NATO reporting name SS-24 ‘Scalpel’), also carrying up to 10 RVs and remaining in service through the early 'Oughts. They also had a significant number of submarine launched SLBMs of significant capability, although the reliability of these systems (and the ballistic missile submarines carrying them) is highly debatable.
Russia has certainly reduced their nuclear arsenals, and their efforts to develop less maintenance-intensive solid propellant ICBMs have been checkered with various failed missile tests. However, the same can be said, to a certain extent, for the United States. The LGM-25C ‘Titan II’ and LGM-118A ‘Peacekeeper’ (50 missiles carrying 10 Mk 21 RVs) were removed from service in 1987 and 2005, respectively, both being repurposed for space launch use. The LGM-30F ‘Minuteman II’ was also removed from service by the mid-2000s, with motors used for various targets and space launch vehicles, while the LGM-30G ‘Minuteman III’ force was reduced to 500 and then to the current 450 (with plans for further reduction), and the three Mk12A MIRV configuration changed to carry a single Mk21 RV from the decommissioned Peacekeeper. On the SLBM side, the entire UGM-96 ‘Trident I C4’ fleet was retired, and the UGM-133 ‘Trident II D5’ reduced in both quantity and number of RVs carried, with some boomers retired or converted to SSGN (cruise missile carrier) duty. So the US also has a substantially reduced (but still size able) nuclear arsenal.
As for the potential for nuclear war, Putin is neither crazy nor stupid. In fact, he has been shown to be a canny manipulator of domestic public opinion with little concern for how clownish his behavior is taken on the international stage, and in fact, the bluster may just be a calculated effort to make him appear a little crazy, just as Reagan deliberately made provocative statements to be seen as a kind of cowboy (albeit, without understanding the full impact of the cultural disconnect). Despite their recent aggression in Crimea and the Ukraine, Russia has no real advantage from instigating a nuclear exchange on any level. In fact, in fundamental deterrence theory, the assumption is that no rational actor will initiate a nuclear attack if there is more than a remote possibility of counterstrike from their opponent or a third party because the consequences are too dire, even against a reduced arsenal. The risk isn’t that Russia or any other nation (even Iran or North Korea) will intentionally start a nuclear war, but that some miscommunication, false positive attack detection, or unauthorized launch of a poorly secured strategic weapon system will initiate a chain of chain of events in which there is not time for the actors to rationally consider the consequences or verify threats. Advocates of “deterrence posture” like to dismiss this possibility as unlikely, but there are at least half a dozen incidences in the last century in which the US or USSR were at the brink of or seriously considering a strategic attack. (In terms of security, it is also worth noting that until 1975 the codes for the PALs on the Minuteman system were all set to “00000000” because the head of the Strategic Air Command didn’t want to risk a delay in the case of garbled transmission of launch codes. We can only assume that up and coming nuclear powers may have similar lapses in nuclear surety.)
As long as nuclear weapons and intercontinental delivery systems exist in significant war, the potential for catastrophic nuclear exchange resulting in the potential for deaths in the hundreds of millions of people exists.