I imagine you might be able to locate flaws with a custom capsule along the lines of a pipeline pig[1]. It would be exceptionally hard to actually fix it from the inside whilst travelling, so you either need to do it from the outside (which requires site access and elevation gear), or bypass/shut down the tube and fix internally.
As Balgair notes, you can get away with a lot on the short run, but leaks are notoriously difficult to patch up. Vacuum leaks are super hard to detect at these pressure ranges, where you're lucky to hear or feel them at all. More than likely, your only indication is to leak helium into the system on purpose and use a mass selector on the outside to 'sniff' for ambient helium (which is extremely rare normally). It's terribly slow and time consuming.
You can always take the short cut and just sorta gunk up the leak to mitigate it, but eventually it'll wear out. Vacuum welds are far better, but also take a lot of skill to perform on the spot: any sort of crevasse will act like a leak (albeit a small one - at these pressures it probably won't matter), so the bead needs to be nigh perfect.
Or you just slam another plate on the outside, glue/weld it up and just sorta not worry about it. Heavy pumping covers a multitude of leaks.
So, young man deciding on the Marine Corp or the French Foreign Legion: Just wait 10 years. Those precision welding jobs 50 feet up next to 1 tor vacuum are going to pay out the bank. Union too, and probably never going away if this thing comes to fruition.
On the other side, Mr Musk gains a hell lot of know-how about plugging vacuum leaks quick, reliably and possibly automatically. Where do you think that might come in handy? Hmmm, on trip to Mars maybe?
I would actually expect leaks to be easy to detect. Just run a high-frequency high-voltage plasma discharge detector on a skeleton vehicle. Wherever the discharge quenches you have a leak. Barcodes laser etched during construction could help you localize the leak to within a few centimeters.
Pinholes might be repairable by pressing a sapphire drift against the leak and melting the metal underneath by shining a laser through.
True, but this either has to be done by paid union labor 50 feet off the ground near 1 tor vacuum or by a heck of a robot. The union guys will be certified up the wazoo and paid to match that and persnickety about it. The robot will be and engineering marvel and a hell of a good idea.
I mention in another reply that Mr. Musk also has plans that involve vacuum differences and not a lot of wiggle room. On a trip to Mars a robot hull fixing machine would sure be nice to have.
[1] https://en.wikipedia.org/wiki/Pigging#Intelligent_pigging