Of course, this affects how the general public perceives bitcoin.
It may be anonymous, but its far from being secure.
Would you mind clarifying what you're meaning by 'it' and 'secure'? To me, the (in-)security of a particular bitcoin site is orthogonal to the security of Bitcoin as a protocol/currency, though the security of bitcoin sites does have a huge impact on mainstream use.
This is not entirely true. When someone is holding a great deal of someone else's money, they can do exactly like banks do and insure their bitcoins, or they can just take the hit and pay for it out of their own pocket, like slush did when his mining pool's bitcoin wallet was comprimised: http://bitcoinmedia.com/compromised-linode-coins-stolen-from... The end user isn't necessarily screwed, and should probably request whoever is holding their money to protect it not only via security but also via some guarantees against the worst case scenarios.
Oh, wait...
When a robber steals money from a bank vault, its not like one day you see. oh shit look at that someone must have stolen my money from the bank. = If someone even robs your safety deposit box, i'm pretty sure that it's insured.
Also when markets collapsed people did and still do bank runs and convert their paper money to gold. So it's not like the dollar hasn't experienced a lack of confidence before.
Currency is all about confidence.