For the most websites, there is no difference between a dedicated vs a shared IP for ranking algorithms.

There are, however, rare cases could make a difference with a shared IP:

1) The shared IP address is hosting sites that are banned for spamming or other reasons (or the IP had such sites in the past). If an IP was blocked for spamming, it can be a big problem.

2) You are expecting to get backlinks from other sites on the same IP or IP address range. Backlinks from the same IP or address range can be discounted under the assumption that one person controls them, thus they have less value.

Both these cases are pretty rare. So, you could get a dedicated IP as an insurance policy, but in general you will be fine on a shared IP.

Yep, if you're sharing IP of spammers it can hurt otherwise it should have never a problem, going to a dedicated server however should justify traffic.

I wrote an article explaining all of this a while back, take a look at it.

[Myth Buster] Virtual Host vs. Dedicated IPs