Are there non-economic barriers to a 1000 passenger aircraft?
If money is no object, and we ignore terminal constraints, then no, there isn't. The A380 already supports 850 passengers in a single-class layout, and Airbus has plans to make a stretched version (the wings are designed to give room to stretch the fuselage without needing too much redesign). 1000 passengers isn't really that much of a stretch; we can basically get there now. The issue is that economic obstacles are very real obstacles to building planes; no one has a need for a 1000-person plane on any route (the A380 isn't even used today with max capacity, it's used to give lots of space to first-class passengers with a bit over 500 passengers).

There are certainly at least two airfields out there that would be able to handle a 1000-passenger A380; unfortunately, neither is a commercial airport (the two are Edwards AFB and the Shuttle Landing Facility; the SLF has a 15,000 foot runway that's 300 feet wide, while Edwards has a similarly-sized paved runway). However, if operation is uneconomical, you won't see anyone building a plane to do it.