I know that plot holes between games are common, but as I'm doing a "full playthrough", just wanted to point out one that leaped out at me as I started in to ME2...
Start of ME2. Scene is set. Miranda and Illusive Man are having a conversation... At the Illusive Man's secret base! And we aren't talking she's there as a holograph, she's physically there. Considering that in ME3 she's supposedly "loyal" to you, and has broken ties with (and is being hunted by) Cerberus, she just might casually mention "Oh, yeah, you know that base you're looking for? It's over at X".