No, you didn't miss anything significant. Joe is a detective and has to consider no matter how unusual the request might appear to Cisco, Wells is a man with secrets. Joe is a detective working from his gut instincts and to him, something isn't adding up.
Joe's thought process might look like this:
Wells' technology created the events which brought metahumans to Central City. He may not be to blame for the problems created by his technology, but the fact he is at the center of the web of events makes him stand out as a potential suspect for a number of issues.
Well's technology (much of which Joe admits to NOT understanding) is both fantastic and frightening in its scope and effect. Barry's powers alone push the boundary of what Joe believed was possible and bring a degree of credence to the stories Barry told him when he was a child. Joe's suspicions are such he even went and gathered up all the previous information and quietly began working the case again.
Given the preponderance of metahuman activity around Wells, Detective West is right to suspect that Wells has kept secrets from him and his staff at Star Labs. The Pied Piper was a former employee with a grudge and the intellectual capacity to stymie Wells, at least from Detective West's perspective.
What tipped West something wasn't right about Wells was the attack on Well's home by the Pied Piper. Wells didn't reveal the cause of the problem and only Barry's forensic acumen tipped Detective West there was more going on that Wells was revealing.
While Joe can't work out the motive, yet, he still thinks it would be best if he could eliminate the man whose technological expertise could render him a suspect even if it happened fifteen years ago, even if he has seen the Reverse-Flash and Wells in the same room at the same time and even if his suspect is apparently trapped in a wheelchair because Wells makes him decidedly uncomfortable both in his capabilities and his contacts.
- And for the record, we don't know for certain that Wells is the Reverse-Flash. We only suspect him. At this point, its circumstantial, at best. Having the gun doesn't necessarily make you the shooter, after all.
- Yes, the actor Cavanaugh (playing Harrison Wells) says in an interview he is the Reverse-Flash but I think this ties the story up a bit too easily. I think there is more to this story. In fact, I believe Harrison Wells is actually a time-traveling Barry Allen.
- If you remember when Wells is in his house and its attacked by the Pied Piper, Wells is forced to move from his chair. Note the super-speed energy depicted is RED not YELLOW. It is only a brief flash of red but enough to make me a bit suspicious. Wells is tall and lanky just like Barry is.
He's also fond of dark, long sleeved shirts...
- What if the yellow suit is more of an exoskeleton, helping Wells to be able to use his speed powers for more than a few seconds without whatever that debilitating issue he is seen suffering from? The suit may have the ability to offer speed powers to whomever is wearing it as well. Hence Cavanaugh's cryptic remark that there is only one Reverse-Flash. What if the Reverse-Flash is whoever is wearing the suit in the future...
And most curiously...
- Last clue: Cisco says the blood on the wall belongs to Barry Allen. An older Barry Allen. We may have been given a "red herring" to make us believe it is OUR Barry Allen when in fact it may be an even OLDER Allen, perhaps even Wells, attempting to ensure the existence of the Flash in the future.