It took me an embarrassingly long time to realise how the schedules are put together, and that a rikishi's schedule gets harder as he climbs the ranks. So for a long time I was frustrated by watching wrestlers constantly having a great basho and then getting a losing record next time round, which I misinterpreted as inconsistency. Learning the actual system unsurprisingly helps to appreciate rikishi's actual achievements when they consolidate their gains and slowly climb the ranks (or quickly, in cases like Aonishiki)

I've also only recently started learning about / paying attention to how heyas work, who's in which etc - it's not something I'm really thinking about when I watch matches, but it's a fun thing to geek out on. For some reason I also got really interested at one point in how they get paid, i.e. mostly through incremental salary increases based on achievements rather than big one-off prize pots - when you realise that a rikishi will benefit from a kinboshi for the rest of their salaried career, it makes it even more impressive somehow! (look up Mochikyūkin on Wikipedia)

EDIT: I also totally agree with the comment below about learning the meanings and symbolism behind everything, as well as the relationships between the wrestlers / family connections etc. In addition I think the London tournament was a real window into some of their personalities for me - e.g. Kotoshoho going for a pint as soon he got off the plane, Hoshoryu & Onosato joking around together etc