If you are going back for a second viewing you are already invested and probably looking for reasons to buy it, rather than for reasons not to. So try and take a parent / friend / colleague who can be impartial and point out things that you may not want to see
Look out for people flying a national flag in their garden
If it is terraced or semi detached, try and suss out sound insulation with neighbours, do you want to hear them arguing, watching TV, shagging?
Check broadband speed, an essential check nowadays
Look at orientation of the house for sunlight. Any seller who knows their stuff will have every lamp and light turned on but how much natural light do you get and are you okay with it
If is a rural area check any local development plans, is that nice field behind the back garden going to become a massive housing estate?
If you have kids, or are planning on having kids, check out the local schools. For me this is the most important thing.
Every house purchase comes with one compromise, usually size of house versus area. You just need to be clear baout which compromise you are happy with.