Could a similar accident to the Ethereum case potentially affect Bitcoin and other crypto-currencies?
Short answer: No.
As I understand Ethereum, its nature is that it provides a distributed programming platform with in-built support for a crypto-currency ("ether"). Anyone(?) can upload arbitrary scripts, which can then be executed by anyone else with an ether wallet.
The serious vulnerabilities found/exploited so far have been bugs in scripts running on the Ethereum platform, rather than problems with the platform itself. No other crypto-currency that I'm aware of provides similar functionality.