Some thoughts on what I think are Eridan's problems:
-He doesn't seem to understand quadrants beyond the basics and probably hasn't even felt or at least can't recognize the feelings they involve, maybe because everything he does is warped by self-pity or maybe because he started dating too young for entirely the wrong reasons (like trying to vacillate to a different one or just ancestor role playing)
-He seems to believe friendship is discount moirallegiance/auspisticism, and moirallegiance/auspisticism is discount matespritship/kismesissitude, just as Alternia intended
-He seems to believe that the only way to keep a conciliatory quadrant from getting bored and breaking things off is by being high maintenance and can't shake off that belief even after he gets evidence to the contrary
-He doesn't seem to understand that people not giving him the kind of attention he wants isn't a reflection of how likable he is or that dating someone doesn't mean they are required to give him the kind of attention he wants
-He rarely pays attention to other people's problems or how they feel, maybe because giving those things a second thought would force him to reflect on his preconceived notions
-He rarely listens to anyone's advice and he rarely learns a lesson from things exploding on his face
-His disdain for low bloods seems to be entirely rooted in the historical enmity between sea dwellers and land dwellers, he has no personal reasons for it
-He seems completely sold on Alternian ideals (like its approach to bigotry, subjugation and romance) even when they don't hold up to examination against his own experience or he's failing to adhere to them
-He's got some unexplained crisis of faith about magic that fucked him up good enough to go batshit with a magic wand and call it science
-He spent weeks on his planet completely alone by his own volition killing monster-like npcs that were pissed at him and apparently whispering some really weird shit, while also failing to cope with a recent breakup
-He spent hours in the lab brooding alone and convincing himself that trying to join some demon that wouldn't have heard a word he had to say before killing him dead was a good idea actually
My observations on how Karkat and Dave's relationship seems to have turned out post retcon
-They're both perfectly at ease with each other while still keeping some of their issues to themselves (Dave with the extent of Bro's abuse, Karkat with anything he deems private or embarrassing enough)
-They're both willing to defend each other from mean spirited comments (Example: Dave defending Karkat's leader position from Vriska, Karkat defending Dave from Vriska being mean about Dave's trauma)
-Following the previous point, they both can tell when the other's actually in distress and they put some work to avoid being the cause of it
-Dave can get Karkat to back down and not waste his energy on a poorly thought out action, Karkat can get Dave to focus
-Dave makes a habit of saying out loud what he thinks Karkat's good at whenever the opportunity arises
-Karkat makes a habit of letting Dave know when he's in the right
-They're both willing to take on activities they don't particularly enjoy just because the other does enjoy it
-They're both willing to take on activities they don't particularly enjoy just because the other seems to enjoy it even less (they've both made comments about Dane Cook movies being bad if I recall correctly, but post retcon they watch them together)
-They both call each other out on their bullshit (and might be starting to develop a system of trying to cut away at the root of it together but it's just in the early stages)
-They refer to the two of them as a unit ("KARKAT: FEEL FREE TO COME AND TALK TO US ABOUT THIS ANY TIME. YOUR SECRETS WILL ALWAYS BE SAFE.")
Reasons why I think Karkat and Jake are similar enough to get along:
-They're both really clever but consider being badass and looked up to a way more valuable trait so they don't show it often and don't achieve nearly as much as they could if they put that cleverness to use
-They're both really emotional and have the habit of retreating to spend time alone when overwhelmed
-They both enjoy fighting (remember Terezi and Karkat on the adorabloodthirsty convo?) and are passionate about terrible movies
-They often draw the short end of the stick
-They're both kinda clumsy
-They tend to hurt people's feelings without intending to by not paying enough attention (or willfully ignoring things they don't know how to deal with) and immediately beat themselves up about it, which makes things worse because the other person's hurt feelings should be the priority
-Their ego and self-respect (and on some level their understanding of who they think they are) took a huge hit during the game and are not going to recover any time soon