The normal cons of working for the government- excessive bureaucracy. It is nearly impossible to get hired if someone isn't pulling you in. The hiring process functions like a black hole- people apply with no understanding of why you never hear back; it is almost completely arbitrary whether HR people select persons for the "certification list" (i.e. the list of applicants certified by HR as meeting standards of the job). HR people don't have proper expertise to make selections and then it is usually personal relationships that determine which arbitrary 3 or so people are called in to interview. Almost every management position is already tagged to a person when it is posted, so most people have no real chance. Also, the complex veterans preference rules end up blocking many, many non-vets because the veterans have a different, lower standard (nothing against vets, those are just the rules).
All of the government hiring rules are complex yet followed unevenly by different managers. So for hiring, unless there is an unusually talented HR staff person working with an unusually knowledgeable hiring manager, the hiring process is just messed up.
It is also nearly impossible to get promoted to the management level of 15 or higher as a staff person. The SEC operates mostly like a large law firm (the enforcement division, made up of lawyers, is the most powerful division of the agency) which is great if you have a law degree, but not so great for everyone else. For example, the vast majority of management roles require a law degree, which isn't really necessary but benefits the law firm structure. Lawyers can also circumvent some of the complex hiring rules which is another reason they hire so many lawyers. The culture is the typical old boys network with the vast majority of senior leaders being white, older men. Some white women have started to rise to management but not consistently. Overall there is nearly zero diversity and zero concern about diversity as evidenced by looking at the numbers; this can be frustrating for non whites who express concerns about this but it is just a fact of life at this agency (not very dissimilar to most agencies as well as private firms).
The normal politics that exist in every corporate structure exist here - however, profit is not the primary motivation. It seems people are more motivated by power, ability to influence the hiring process, politics, and keeping their jobs (also normal government "cons").
There is a lot of uncertainty given that the SEC is part of the government appropriations process - when the government shuts down, staff might not be paid. This can impact your life constantly and drastically in terms of not having dependable income, needing to rely on credit cards, taking months to "recover" after you haven't been paid for months, etc. While it doesnt happen often, when it does it can be a disaster. The uncertainty about funding also leads to inefficiency in operations--the agency often doesn't know what money is coming in and when so hiring and major projects get put on hold or thrown off schedule.
Having worked at multiple government agencies, the SEC seems like the least bad in terms of all the typical government problems (bureaucracy, pettiness, bad staff/management who can both hold on to jobs for too long, funding problems). Staff seem more knowledgeable than at other agencies and people do get fired or removed for poor performance. Another con though is that there are certainly those few government staff, often in highly paid management, who are just hanging around and should have long since retired. Overall, people care about their work more than other agencies, but things still move ridiculously slowly.