Loyalty mission consequence?

Only for opening up rank 6 powers as far as I can tell. Peebee's mission was bugged in my first game so I never did it. You can still work on their loyalty missions after beating the game, too. There isn't a way to prevent someone from joining your ship either -- can't turn Vetra, Drack, or Peebee away.

Captain Dunn dies if you don't do Cora's loyalty mission, but that's about it.

There are narrative consequences to the loyalty missions. Depending on the decision you make in Jaal's mission you can't romance him anymore, Cora's missions impacts who is the Asari Pathfinder & the end mission, doing Drack's mission means Kesh will introduce you to her clutch etc. 

I prefer this approach to ME2, where basically you have to do the loyalty mission & 100% agree with them (with the exception of Zaeed) or they die horribly. 

Nah, I didn't like the idea of "unless you help me I won't put in as much effort on a suicide mission."

Captain Dunn survives if you have the three pathfinders together, so you have to force Avitus to be the turian pathfinder, have Raeka/Hayjer and Sarissa/Vederia. It doesn't matter who is the salarian and asari pathfinder as long as you convince Avitus.

Interesting, thanks for the info.

There's no obvious consequences, though I wonder if it'll come back to bite you in the sequel. Like how mass effect 2 loyalty missions could effect who lives or dies in mass effect 3.

That's a thorough list.   I have to say, though, that the difference between stupid Liam and less-stupid Liam is too subtle for me to discern. I guess the lack of crises caused by Liam in the back-half is a sign of growth.

Dunn dying because Sarissa is not in the picture and sufficiently motivated is the only consequence of the Cora LM mission. The others have no consequences. In fact you don't even have to do any of the vaults or fix any of the worlds except for Eos. You can shortcut most of the content and get the same ending in what some said was a 9-hour game. I plan to try this myself as I am disatisfied with most of the LMs and sidequests (most of the game for that matter). For example if I can't get Sid fired or demoted at the end of Vetra's LM, I'd rather not do it at all. Same with Dr. Kennedy.

If you already had a sufficient paragon score, you could screw up his mission and he was OK with it. Same with Miranda or Jack.

At times that option would be usefull. They're absolutely useless in helping to fight architects or those Kett leaders in their bubble, since they don't aim for the vulnerable spots. Apart from the fact that video games these days feel the general need to single out the player with their attacks and largely leave your companions be, if they're not standing right in their way.