I'm certainly no expert in this, but from what I've read it's pretty complicated. The sense I get is that it matters who and what you criticize more than how often. In fact, lots of "self-criticism" was encouraged and even seen as patriotic.
Stalin encouraged a lot of criticism to be directed at local officials. So, while it would probably be pretty dangerous to criticize Stalin or the communist party/project/ideology itself, complaining about local corruption and bureaucracy was great. Stalin would actually use local criticism to help justify some of his purges and other political maneuvering. Contrary to what you might expect, being excessively bureaucracy was seen as anti-communist: the idea after all was for the government to phase itself out.
This paper is about family law and direct participation around that.
This one is much much longer but it goes into all of the different types of popular participation allowed in the Soviet Union. Here's a quote from page 18:
"The public discussion of the draft constitution harnessed these earlier practices and trends to engender support for state-building projects, and to rein in the local and regional officials whom central authorities had trouble controlling. The central, regional and local press solicited letters, many of which documented how the authors’ lives had improved under the Soviet system and how the rights guaranteed in the new constitution promised to further enhance their quality of life. Lesson plans designed to guide the discussion of the draft also focused on the increased quality of life for workers as well. Additionally, during the discussion of the draft constitution, participants were encouraged to criticize local officials who had been lax in fulfilling their duty, and to replace them with more competent and politically active representatives. This trend was not an afterthought, but one of the main reasons that the party sought to expand the franchise in the first place. Stalin and other leaders felt that by making the Soviet system more participatory, it would enable the masses to police and remove unsuitable local representatives. Sheila Fitzpatrick addresses this trend in her article “How the Mice Buried the Cat: Scenes from the Great Purges of 1937 in the Russian Provinces.”34 She notes that, as the local party and state apparatus grew increasingly beyond the control of the central party and state leadership, central officials turned to increasingly extreme means to control them, including encouraging local workers and officials to denounce their bosses publicly. In the Road to Terror, 35 Getty and Naumov note the same trend. Central officials called for denunciations of local and regional party and state officials in the wake of unfulfilled campaign goals and increased unresponsiveness to central demands."