The telemetry and tracking itself for the laser links. All the satellites need fairly accurate orbital information from all other satellites; there will be several thousand satellites capable of performing autonomous orbital adjustments to avoid debris and for their own station keeping. There has to be a convenient and reliable fallback for automatically syncing satellites with the rest of the network after a reboot or loss of communication.
The packet network needs to maintain an efficient routing table and provide low packet loss to end-users. My guess is that the only practical choice will be establishing a large number of point-to-point channels with their own retry/error-correction management. TCP/IP isn't capable of dealing with more than about 1% packet loss and I doubt raw optical/wireless links will be reliable enough especially with topology changes, requiring extensive store-and-forward hardware to buffer transmissions waiting for a reliable route or de-duplicating multicast packets at the receiving end. Reassembly and de-duplication on receipt is theoretically feasible; if a tight reception window can be maintained then specialized hardware could filter duplicates sent over 2 or 3 redundant routes to a local receiver without increasing observed latency or using unreasonable amounts of RAM. A combination approach could allow a tradeoff between using double or triple the raw bandwidth but providing low-latency reliability vs. higher latency with retries while maximizing throughput depending on the current network load. It could also be hardcoded for different traffic classes.
I'm not involved in this problem space in any technical capacity but it sounds like a very fun set of problems to solve.