Bitcoin's fundamental core strength is being distributed. That's also the thing that makes it mostly unusable.
Sure, if I just trust someone else to manage my wallet and verify the block chain for me, it becomes usable. This is the exact reason why people keep getting taken by bad "online wallet" services -- they can't bear to do it themselves.
Mobile wallets are a great example. There are two types of mobile wallets: the kind that wingnuts struggle through using because they're bitcoin fanatics, and the kind that are actually interesting for people drawn to convenience. The former actually verify the block chain, the latter are a thin client over an API to someone else that's managing that off the device.
With Bitcoin you CAN run your own node, you CAN mine your own blocks, you CAN verify the integrity of every transaction that every person has ever made in the blockchain, but that does not mean that you HAVE to do these things. Because this is an open-source currency, WHEN you choose to yield to a third party, you get to choose one based on their merits because the barrier to entry to become a service provider is so low, thus competition is fierce. Compare with the banking oligopoly.
This is on par with Linux. You CAN build every binary on your machine from source, but you do not HAVE to and most people choose to yield their compiling duties to distributions and just install pre-cooked binaries. The benefits of open source continue to shine upon these people, because they get to choose their distribution, and they benefit from the fruits of the bazaar development model even when they are not actively engaging in it.
The multibit client is a much better, though still reduced-security, option.
The sync comments there are outdated— I installed a new Bitcoin node two days ago and the sync only took about 2 hours from nothing.
Even if it "only took about 2 hours," we're living in a world where companies are living and dying by shaving 30ms off page load times and a/b testing the color of their signup buttons.
Wrong client. Try blockchain.info. Instant sync.
"You can purchase some bitcoins, which involves..."
Wrong method. Try BitInstant. Instant.
"Wait 50 minutes to get enough verified transactions..."
Could be a few seconds. As a seller, you can choose the number of verifications you wait for. My web shop waits for the first only (fine for sub $100 purchases), so verification takes about 5 seconds. If you wait for 10 verifications, well, yeah it's going to take a while, but you don't need that level of security unless you're buying a house.
"All of this would be completely impossible on a mobile device."
Er... Google "site:play.google.com bitcoin"
Loads of mobile wallets.