"The government" is too heterogenous of an entity to comment on. Which government? The local city government? Specific departments within that local city government? The state government? Specific departments within said state government? And so on and so forth.
On the whole, I trust any and all government agencies that are staffed by relevant and well-qualified professional experts. Which is the majority of them, honestly. I trust the department that handles electricity in the city I live in to do their job well... and they do. They're professionals and experts in that kind of engineering and civil service. I trust the wildlife biologists employed by the relevant state agency to be well-appraised of the state's native wildlife and know a lot more about it than I do as a botanist, because they DO know more about it than I do. I trust the folks working at the Center for Disease Control to be following the latest science to the best of their professional ability to manage communicable diseases for the nation... and they do that. Scientific and technical professionals are, as a general rule, very, very trustworthy. Because we don't give a crap about playing political games (and become extremely frustrated when said games get in the way of us doing our jobs well).
On the whole, I trust those holding elected office to be overly-concerned with re-election and not focused enough on doing their actual jobs as civil servants, because this happens far more often than it should. Less so at the level of local governance than state and federal, however, which is an important distinction. The real problems happen when civil servants are elected who are incapable of actually being civil servants. Being a civil servant is all about serving something greater than yourself. An elected official who serves only themselves should be fired immediately, but unfortunately, that's not how it works in this country.