Why Intersect gives ERROR 999999: Error executing function Invalid Topology [Too many lineseg endpoints]?

Very few contiguous cells in a detailed DEM will have identical values of both slope and aspect. Therefore, if the input features represent contiguous areas of common slope and common aspect, we should expect the result of this intersection procedure to have, on average, almost one feature per cell.

There were originally 65,000 * 1000^2 = 6.5 E10 cells in the DEM. To represent each of these requires at least four ordered pairs of either 4-byte integer or 8-byte floating coordinates, or 32-64 bytes. That's a 1.3 E12 - 2.6 E12 byte (1.3 - 2.5 TB) requirement. We haven't even begun to account for file overhead (a feature is stored as more than just its coordinates), indexes, or the attribute values, which themselves could need 0.6 TB (if stored in double precision) or more (if stored as text), plus storage for identifiers. Oh, yes--ArcGIS likes to keep two copies of each intersection around, thereby doubling everything. You might need 7-8 TB just to store the output.

Even if you had the storage needed, (a) you might use twice this (or more) if ArcGIS is caching intermediate files and (b) it's doubtful that the operation would complete in any reasonable time, anyway.

The solution is to perform grid operations using grid data structures, not vector data structures. If vector output absolutely is needed, perform the vectorization after all grid operations are complete.