Arsenal has, in my opinion, been pretty awesome and had some great moments in the relaunch. Even so he has done a few things that have caught my attention.
In Red Hood and the Outlaws Roy is the only one out of the three leads that isn't a loner by choice. Kori went into a self imposed exile and Jason struck out on his own due to his moral code. Roy clings to his friends but as we see in the Death of the Family cross over in RHATO #15 he's a little more obsessed than we assumed. Kori and him are together when the ship broadcasts a message Bullock sends Jasons' cell. Once it ends Kori asks him why Jasons' phone is linked with the ship. Roy admits he used Cruxs' tech (*1) to connect to the messages and alert him to the important ones. Kori is bothered by this and hopes he doesn't keep track of her. His reaction seems to imply he does.
There are a few reasons Roy might feel compelled to do this. Firstly his bad experience with Oliver Queen. In this universe Ollie was his boss and a lot of problems stemmed from Roy not voicing his problems until too late. Lobdell has confirmed in interviews that the character has no filter for what he says because of fearing history repeating it's self if he remains silent. Ollie also kept his identity a secret making him realize his inventions were being exploited and their relationship wasn't as stable as he hoped. Both of his friends have things they don't talk about although Roy knows a good deal before they decide to team up.
Still there could be trouble popping up because he doesn't have all the information. This may be a misguided way of protecting them. In the first issue Jason tries to leave them without a word to track down his teachers killer. (*2) Jason is against them helping him and despite warming up to them still has a tendency to act like a loner. Roy may think he's protecting him and Kori by invading their privacy. Perhaps Roy also fears his friends abandoning him and wants a heads up to see if he can fix whatever problems occur.
In Red Hood/Arsenal Roy took off on his own after the break up with Kori. Jason saves him and Roy instantly decides they should both go legit. Moreover he knows he can talk Jason into it even through his buddy is against the idea. In the second issue we learn Roy has managed to convince Jason to be his roommate. Which doesn't seem like a bad idea since Jason is always busy and they were techically living together with Kori before. Except that the spaceship had more room and now Roy doesn't let him have much privacy. More disturbingly he often tests out his inventions on Jason and if their anything like the flamethrower that means he's endangering his best friend on a regular basis.
This could be thoughtlessness on Roys' part due to him being overly eager to try out his creations. But consider this: when the three of them lived together this never happened. He was usually shown working alone and explained what he did later. While he confessed to wanting attention in his narration boxes back in RHATO he's never been this desperate at getting it. Not with Kori or Jason at any rate. It does seem like he's trying harder to prove himself since Kori left. With the hero for hire idea and his inventions. Roy doesn't see anything wrong with what he did, in fact he seems to be trying to sell it off as a good thing.
He actually seems put out that Jason doesn't appreciate his efforts enough to thank him. Then he reminds him of all baddies they faced together before saying this:
Roy Harper: "Because you have me looking at the big picture!"
This stuck me more than any other part during the shower exchange. It sounds like he's trying to convince Jason of something. Maybe to prove they make a good team even without Kori? That like a bat Roy can be prepared for anything? Yet he's so focused on what he's attempting Roy misses the big picture by spending all the money on parts which shows him in a pretty irresponsible light.
It's doubtful that we'll ever find out if Kori brought up the phone tap again. I think Jason should know about it though since he's one of the bat kids. Despite the tech in Cruxs' ship being alien Tim Drake was still able to figure out Jason was listening in on Alfreds' message. Jason should know but that doesn't mean he'd do anything about it. We all know how Batman tended to get into everyone's business and in a weird way Jason might translate that to Roy giving a damn about him. He might have thought it was a good idea in case he ran into trouble. Interestingly Jason saw the dangerous potential of the tech before deciding against using it himself (at least at the moment.)
There's a lot Jason puts up with just two issues into RHA. I think he would be far more upset with Roy invading his privacy and risking his life in that last series. He's cutting a lot of slack given Kori leaving and how that affects Roy. In fact it's suggested that's why he's going along with all of it. Part of him likely believe Roy would never really hurt him or he's smart enough not to. During their trip to Paris he also notes Roy acting girl crazy when that isn't how he normally acts.
Personally I like this storyline of Roy struggling with his problems and Jason being the one to help him out. It's the kind of growth many unfortunately can't see within Jasons' character and shows promise for both leads.
*1 This tech taps into any communication channel making it easy to eavesdrop. It's how they accidently picked up Alfred's distress message at the end of #8.
*2 How Kori and Roy found out what he was doing and were able to assist him was never revealed on panel.