What scenario could a lack of bitcoin full-node cause problems in the network? Let's say the only full-nodes in the network were the mining nodes. If you joined the network as a full-node, what problems or attacks could happen in such a scenario? Also, what problems or attacks could happen to SPV clients that aren't already likely in the current network environment? 

At what point are these problems or attacks likely to start happening in terms of number or percentage of the network's full nodes run by independent people/entities?
By running a full node, you ensure that your bitcoin transactions are valid and received by the network, and that your bitcoins are 'playing by the rules you want' (you implicitly agree to the rules of the code by running the node). 

So if you are not running a node, you are depending on other nodes in the network to relay this information to you.

The less nodes that exist, the easier it would be for a majority of nodes to coordinate and change some rules, and so users that are not running their own nodes may then unknowingly have the rules changed on them.