I wouldn't really worry about morning wood, dude. I mean, I rarely wake up having a morning wood, but I have no troubles whatsoever having it up at 100% when so called for, and I also get turned on easy. (Like, from my girlfriend simply sitting on my lap - something I thought would not happen that often at 24). About the morning woods: I notice I get them when I wake up to an alarm clock and likely will be interrupted from deep sleep, but I don't get them when I just wake up normally, which is 99% of my days. (As I do some translating from my home and also have lectures during the afternoon/early evening only, which is lenient as hell on my sleeping).
Watery semen is also something that still affects me after nearly 14 months of finasteride-use, though the texture has become a bit better with the passage of time (compared to having just started finasteride), but I am not worried about that. What I do worry about is able to get hard when I want to be hard and actually having sexual desires. Those are still there, so some watery semen is "whatever" to me, as I know you can still conceive a baby with no problems on finasteride.
So with all this rambling in mind, you'll know your own body better than anyone else, but I would say observe it a bit, unless you are really worried about your erection quality. How's your diet? Amount of sleep? Stress levels? Any change from pre-finasteride times?