After a few quick searches for 3G security I was able to learn that this standard uses the KASUMI block cipher, of which several weaknesses have been identified (although apparently none of practical use in decrypting 3G traffic?). Anyway, this made me curious - what kinds of security measures are in place for 4G LTE?
Information regarding the current implementation of "4G" LTE, as well as the soon to be deployed true 4G LTE-A, can be found at the European Telecommunications Standards Institute (ETSI) website and portal.
3G networks use the KASUMI block cipher with the UEA1 confidentiality and UIA1 integrity algorithms. As you said, there have been several demonstrated weaknesses, which has prompted the use of a new cipher / algorithm.
The 4G LTE successor is the SNOW 3G stream cipher and the UEA2 confidentiality and UIA2 integrity algorithms. To quote the specs page:
At a high level, 4G uses symmetric-key cryptography to (1) authenticate the subscriber (phone), and (2) encrypt data sent over the 4G wireless link.
While there have been academic "weaknesses" in KASUMI found, none of them have any practical relevance to the security of 4G in practice. For instance, one of the known "weaknesses" is a related-key attack. However, related-key attacks are only of relevance if the system uses the block cipher in an inappropriate way. 4G does not make this mistake, so related-key attacks are of no relevance. As Wikipedia says, "The authors note that this attack may not be applicable to the way A5/3 is used in 3G systems" (and the same applies to 4G).
The primary weakness in 4G security is that its use of cryptography does not provide end-to-end security. It only encrypts the traffic between the phone and the base station, but there is no encryption while the data is communicated over the wired network. This means that there is no security against a malicious or compromised carrier (or a carrier who is sharing all of your data with the local government), and no security for your data when it transits the Internet or the rest of the path. So, if you want security for your data, you need to do your own end-to-end encryption, e.g., using SSL/TLS, SSH, a VPN, or a similar mechanism.