Well, we haven't seen any kind of legislative assembly, but Equestria definitely has large cities and a mayor in ponyville as opposed to strictly being based on feudal nobility. Also, the Smile Song has a pony with a gavel cutie mark. So I'm fairly certain that Equestria has courts and judges to resolve the serious pony disputes that fall short of directly petitioning Celestia herself. Mostly issues as to inheritance and title to land I would guess.
Then, I like to think that Celestia does take an active hand in ruling, allowing direct petitions for a limited class of serious cases, probably mostly relating to defense and magic, but also for ponies that are in distress and need her direct intervention (such as the Phillydelphia parasprite infestation mentioned in canon). Spike, being a direct backdoor to the princess, is actually far more valuable than he realizes.
For local governance, I think that we're on a system of locally elected rulers who serve at the pleasure of Celestia. That is, Celestia is the absolute monarch, but she allows each community to govern itself at its own choosing and only intervenes for important kingdom-wide edicts or the personal petitions noted above. Celestia also administers the court system directly and appoints all the judges.
Given how we saw Luna going in and out in the Royal Wedding episodes, I like to imagine that she's serving the kingdom as a combination diplomat and circuit judge, actually traveling around Equestria and visiting the various towns and cities to provide aid and dispute resolution for a limited time before moving on to the next city. Probably she goes to each area for a few days a month.
The Sun is Hot.
Interesting, I'll read this later.
Considering our pre-orders scared them into delaying the release date due to the unprecedented large numbers, I don't think they need to worry about all the neighsayers.