It's extremely unlikely there's a big problem in the sense that you mean it. The Model 3 is easier to produce than the Model S and less complex. There's practically nothing new on the Model 3 that would plausibly be a big thing that's not working as to hold everything up in the scandalous manner you're implying (leaks, hand-building, not working, big problems, oh my).
More likely is that Musk set an overly ambitious target, for the hundredth time, and what they're doing for the quarter they probably should not have been doing at all. They produced something like 60-80 Model S vehicles in the first month. Check back in two quarters, if the Model 3 production is down 80%-90% from projections, that will be something meaningful.