Every system has some weaknesses. Similarly, Ethereum also has some weaknesses. Obviously, just like any other application, Ethereum source code can have bugs. And also just like any other network-based application, Ethereum is also exposed to DoS attacks. But let's see the unique and most important weaknesses of Ethereum.
An attacker can attempt to fill the network with regular nodes controlled by him; you would then be very likely to connect only to the attacker nodes. Once you have connected to the attacker nodes, the attacker can refuse to relay blocks and transactions from everyone, thereby disconnecting you from the network. The attacker can relay only blocks that he creates, thereby putting you on a separate network, and so on.