It would be worth getting an expert to 'diagnose' the patchiness. It's probable that some of the old finish is still on it, but there are other possibilities too. For example, I notice that a lot of the darker areas are just in front of the door. If the finish wore off there a long time ago, then the extra dirt/UV light could have made that part of the wood go a lot darker. Another possibility is pet stains (wee) darkening worn areas.
I think it's a classic case of the renovator's dilemma - either you spend loads of time researching and sorting it out yourself, or loads of money getting a pro in.
If the finish wasn't particularly worn before you started, then my first guess is probably accurate, and you could improve the living room's chances with a belt sander getting all of the old finish off. Test by spraying water on and see if any patchiness shows, and also whether the water is absorbed evenly. If you've only got an orbital sander then forget it or buy/borrow a belt sander. You could also improve things with some wood conditioner, but test that on an area that is likely to be covered by a sofa first.
One last thing - stains and stained varnishes really show up imperfections and old finishes. So rather than go darker, it'll look much more even if you use a clear varnish.
Finally, there's a lot to be said for Jacob's and Phil's comments.