What scenario could a lack of bitcoin full-node cause problems in the network?
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.