Using funds that have not been completely transferred yet for a new transaction What happens if I start a new transaction with funds from a transaction which isn't 100% complete? 

Let's say, the incoming transaction shows 2/3 of the green dot, but the sum is counted as full by my Bitcoin Wallet for Android.
The green dot in Bitcoin Wallet for Android represents the number of confirmations an incoming transaction has. Once the first slice appears, the transaction has its first confirmation; i.e. it was included in the blockchain. Additional slices will appear when succeeding blocks are found, AFAIR marking up to six confirmations.

There should not be any issue or delay to spending any funds that have at least one confirmation as long as you include a sufficient transaction fee.