So I quick note about the spy in question - he was Adolf Tolkachyov (born in my adopted "hometown" of Aktyubinsk, aka modern-day Aktobe, Kazakhstan), who was an electronics engineer who passed information on Soviet radar systems to the CIA. He was arrested in 1985 and executed the following year. The CIA itself, reviewing a book by David Hoffman on Tolkachyov, notes that his intelligence saved an estimated $2 billion worth of US research and development in his first two years of cooperation alone, and arguably accounted for the overwhelming victory by US aircraft over Soviet-made, Iraqi-owned MIG It's worth noting that part of the reason he no doubt was having issues spending the money is that he kept his espionage work secret from his own family (ostensibly to protect them from also being punished should he be caught), so one's issue of trying to spend a boatload of money is compounded when even your own family cannot know about it.

But that's not the OP's question, so on to that aspect. The Soviet Union in 1985 indeed was a place with a distribution of incomes, but an extremely small portion of the population, around 1 percent, would have received 300 rubles a month, or 3,600 rubles a year. So a million rubles would be almost 300 times what even a very elite few could expect to earn in an annual salary, even in Moscow. In comparison, for the USSR as a whole, about 54% of the population would have 100 to 200 rubles a month, and something like 28% of the population would have earned less than 100 rubles a month. Indeed, the first Soviet millionaire (in legal terms, at least) would not come into being until Artyom Tarasov reached that income level in 1989, paying himself 3 million rubles from his business (he ended up leaving the country the following year because of conflicts with the government over his business).

On the consumer end of things, could you just go out and spend a million rubles in 1985? It would have been much harder than someone living in a market economy might expect. As I discussed a little in this recent answer, part of the issue around this is that, with some extremely limited free market exceptions, most domestic goods produced in the Soviet Union for consumers were produced and distributed by state agencies or enterprises. So in many ways the price of a good, like say for a television or a car, or even a vacation at a Soviet resort, was the least of a consumer's concern - prices were all ultimately set by GOSPLAN (the state economic planning agency....ok very technically it was Goskomtsen or the State Committee on Prices that did this). The issue was access to the goods, as usually one had to either put themselves down on a waitlist, or use blat connections (relationships with friends, family, or even managers or other well-connected "patrons") to get access to the required good. Bribery could of course play a major role in getting access to something, but monetary bribery wasn't necessarily the way one wanted to go about it - again, money was only of so much use, and too much money could raise questions. Useful services or valued goods would actually be a smarter bet than cash. Was Tolkachyov well-connected? As an electronics engineer working in the defense industry, no doubt - but of course even if he knew a friendly general or two, showing up with a million rubles, let alone a huge quantity of anything else, would raise a lot of questions and get everyone in the transaction into a lot of trouble.

Well, alright, so much for domestic options: what about international options? Soviet citizens most certainly would buy foreign goods when traveling abroad, but getting an exit visa allowing foreign travel was a long and arduous process that was reserved for only the most demonstratively loyal of the elite.

So maybe not that option. What about if someone wanted to buy (usually better quality) foreign goods, like a Japanese tv and have it imported and shipped to them? Here again there were major obstacles to spending your Soviet millions. The Soviet Ministry of Foreign Trade (Minvneshtorg) maintained essentially a monopoly on all import and export trade from the Soviet Union, so a Soviet citizen couldn't just order something abroad and import it - legally, at least, but more on that to come.

OK, so I can't order my Japanese tv abroad and have it imported - can I pay for one that is already legally imported into the USSR? Maybe. There were stores in the USSR that sold goods, especially sought-after imported goods, for hard currency (meaning - not Soviet rubles), and these were the Beryozka chain of stores. Great, so I can get my CIA handlers to pay me in dollars instead and go shopping, right? Not so fast: access is more important than cash, your average Soviet citizen couldn't just walk into the store off the street and buy something, they had to be on a list of approved Soviet citizens who were able to exchange that foreign cash for a purchase. And not just any Soviet citizen could have foreign currency (I mean, what are you? A spy?)! A major issue for your Soviet spender is that the Soviet ruble simply was not a convertible currency: a Soviet citizen couldn't walk into a bank or a foreign exchange booth and get foreign currency.

Of course, illegal smuggling and currency exchange did occur, but this was largely treated as "speculation", or as economic crimes "against state and public property". An economic "crime" in excess of 200,000 would de facto guarantee the accused a death penalty, as was applied famously in the Rokotov–Faibishenko case of 1961, where a ring of speculators were buying and selling foreign currency for a profit in Moscow. Perhaps a few thousand individuals were executed for similar economic crimes in the quarter century that followed. So even to illegally spend your million rubles, you'd effectively have to get involved now with a ring of organized criminals and again risk the death penalty.

Frankly, no wonder this sounds like too much work. Tolkachyov claimed to be providing intelligence to the US because of anti-Soviet ideals, in the spirit of Solzhenitsyn and Sakharov. But even if this were not true, it would simply be easier and safer to stuff his million rubles under the sink than to try to go out and spend it. Trying to go on a shopping spree in the USSR circa 1985 wasn't as simple as going to the mall: it involved spending a lot of time, energy and social capital, and too much economic activity, especially in the millionaire range, could be as detrimental to your health as, well, spying.