One thing I liked a lot about ME2 was that I didn't have to hunt across a whole planet to find side missions. When you began a scan the landing site would pop right up. I'm hoping it is, but I figured I'd ask, is it the same, or do you have to scan around each planet? Or is it completely different?
Scanning a planet now gives war assets and other rewards.
Planet-scanning for "treasure" returns, but is vastly improved over what it was in "Mass Effect 2." Rather than having to survey and mine each planet for resources that may or may not be there, players can scan the system and find loot much faster than before. The treasure can be war assets (which are important in the final scenario), artifacts that can be sold or traded, intelligence about different factions or fuel for your spacecraft -- a welcome improvement from an experienced player's perspective.
I do not believe there are any side-missions obtained from planet scanning in ME3.
Most side missions are obtained from a small set of methods
Eavesdropping: Walking around and listening to the conversations of others, without engaging them in dialogue. Especially in the Citadel, for example walking around the commons
Dialogue: Usually with minor characters, though the ultimate impact of the side quest may be notable. For example to initiate the Hanar Diplomat side quest you need to talk with Kasumi outside the C-Sec office.
Some side quests appear solely as responses to other side quests being completed
While the main line quests are labelled Priority: the side quests are labelled in a variety of manners, which often suggests their origin; Citadel: missions usually are obtained on or completed at the Citadel, N7: missions often appear in your journal as a response to other missions or Priority milestones, Name: missions are usually scanning or short combat missions if the name is a sector or planet or a sequence of interactions and sub missions if it's a person's name (eg Aria's quests).
A reasonable list of missions can be found at the ME Wiki.