When the last bitcoin is mined will everyone know it? The total number of possible bitcoins is limited. This means that at some point the last bitcoin is mined and no more bitcoins will be mined after that moment.

When this happens will we notice it and how?
Some time in around year 2100, blocks will only be worth 0.00000001 BTC or less. But a long time before this, miners will earn their bitcoins by the transaction fee. And when blocks no longer can generate bitcoins, then the miners will earn their bitcoins only from the transaction fee (versus earning 99.99% from the fee). Miners can still generate blocks, even though blocks no longer generate new bitcoins.

The bitcoin-qt client does not have any "popup window" when this happen, if that's what your asking?