Any migration carries some degree of risk and short-term consequences; a move to HTTPS is no exception.
Rand Fishkin wrote an interesting post on Moz's experience moving to HTTPS. The short version of that story is that they initially lost about 11% of their organic search traffic, but recovered within 3 months. So yes, there can be at least some short-term negative effects.
It depends on your circumstances, but usually if I was considering a move to HTTPS I'd want to migrate the whole thing. It's very easy to end up in the situation where the 'secure' pages carry insecure elements, such as images served from a different (http) URL on the site. Users will see messages in the browser about not every element being secure, and you've left an attack vector of sorts there. So if you're doing a partial migration only, you do have to be particularly careful.