I'm not concerned about any of it really except the deer thing, but even here, was he just repeating the story to you for something to talk about, knowing full well you were there? I know someone who has always done that, even when she was in her 30's, she's now mid 80's and this is normal for her. She knows you were there but she still wants to recount it as if she's telling you something, really just wants to relive it and talk about something. Did he just want to recount the story for something to talk about again?
If he cannot remember that you were with him I think that's of some concern, but that doesn't mean he's going to deteriorate, dementia is very individual in how it plays out, depending on type and depending on the person.
I'm not concerned with the hot cross buns unless all the pictures were really obviously christmassy ones. To him it was just a picture? May have not made the connection that they are supposed to be christmas pictures even though he knew it was an advent calendar.
The birthday dates, it's not unusual for older people to forget or not focus on the date, just the birthday, so I wouldn't worry too much about that.
Saying 'happy birthday' could be a slip of the tongue, did he correct it? Slightly concerning, would have to have more slip ups to know on that.
Urine infections can knock an older person for six and cause confusion in them even when they definitely don't have dementia, so it's important to know this going forward (even if not something you'd ask about now). I've known elderly people develop sepsis from a urine infection and the family thought they'd suddenly developed dementia.
But back to your concerns, overall I'd say a lot of this might just be being a lot older than you. Details become less important (been there, done it) and that's normal (hot cross buns example). But you're right to keep a check on this.
I would encourage him to get a blood test etc, just suggest it as an MOT. I wouldn't yet speak to him about your concerns. From what you say it may still be nothing, and if it is something developing, maybe he doesn't have to be worried about it just yet. But if you later become sure there's something wrong, then it may be worth getting him checked by a GP as there are medications now that can slow cognitive decline down. I hope all is ok though.