I don't see why anyone should be upset with Leli at all, to be honest. lol
Solas never did anything to indicate that he was someone Leliana should expend valuable time and resources checking into. Yes, he showed up practically out of nowhere in the middle of a crisis to offer help, but he did exactly that, and continued to do so after the initial attempt to close the Breach. Why would she waste time and effort checking up on someone who wasn't hindering the Inquisition's efforts? She had much more important things to worry about than someone who was helping being a little shady (I mean hello, she's pretty damn shady herself). If Solas had ever actually done anything to harm the Inquisition in any way, I'm pretty sure Leliana would have investigated him and his claims much earlier.
The same goes for Blackwall. It benefited the Inquisition to stay quiet about his true identity, so that's what she did. When his true identity comes out, what happens? Well... if you utilized those Warden treaties when you first recruited Blackwall, people get angry about that. If you use the Inquisition's influence to get him out of jail then - you guessed it - people get angry. You then have to waste time and resources placating those people (well, you don't have to, obviously... you can ignore all the war table missions if you really want to) while you're still in the middle of dealing with Corypheus.
So yeah, I don't blame Leli for putting Solas investigations on the back burner at all. A slightly shady elf who's still being super helpful was the absolute least of everyone's worries.
I absolutely disagree. It all could of blown up in her face. Both Blackwall and Solas could have had more sinister motives than they did. They could of done real harm to the Inquisition and the Inquisitor. Leliana was the spy master it was her job to seek out ALL POSSIBLE threats. If she's letting these sketchy, but helpful at the time people go along with their business without doing anything, who else is she letting get away with it? This is wartime for the Inquisition there is no time for stupid mistakes or Leliana taking it upon herself to make these judgment calls (the Inquisitor is the leader for a reason). The very least she could of done was tell the Inquisitor about Blackwall (and let the Inquisitor aka the person in charge aka the person travelling with Blackwall aka possibly the person sleeping with him! know who he really was and let her/him decide what to do). With Solas she seriously should of checked out his story before he went on off and disappeared. I mean, I love Solas, but he was the cause that led to the Breach, which means he's at least a littke responsible for all the deaths caused by it. And he has ulterior motives, and...you know he's an ancient elven "god". These might of been important pieces of information to find out. I'd also say that Solas was veeeerrryy suspicious. All his super convenience with timing and " oh, I learned this in the Fade...uh, that too, in the Fade...THE FADE!". Very suspicious, I think I.B. and even Blackwall pick up on it a little bit.
Again, I do like Leliana. She's up on my favorite Dragon Age characters list, but not a good spy master. Not at all.

Although she definitely looks the part