I think there were a few less wires in the Star Trek sickbay!!!
But, obviously technology is changing. Every ER patient is now routinely connected to an EKG, Pulse-OX monitor, and automatic BP cuff, all with alarms and central monitoring. And, I can imagine more real-time testing and monitoring being added to patient rooms in the future.
Of course in Star Trek, they just waved a tricorder in front of a patient to immediately assess all vital information. And surgery and injections were done without penetrating the skin.
I could imagine that a CAT scan or MRI might become a routine part of future admissions. And a computer could potentially do a better retina scan than a doctor is able to do, as well as saving images for future reference.
Some of the new MRI machines are much less tube-like than those in the past, but they are still a bit bulkier than the Star Trek scanners.
I could imagine bedside labs becoming routine. Patients with a catheter should have accurate real-time monitoring of kidney function, WBC, and bacteria, without ordering labs.
Blood may still need to be taken, but wouldn't it be nice to get instant analytical results.