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:
SNOW 3G is a word-oriented stream cipher that generates a sequence of 32-bit words under the control of a 128-bit key and a 128-bit initialisation variable. These words can be used to mask the plaintext. First a key initialisation is performed, i.e. the cipher is clocked without producing output, see 4.1. Then with every clock tick it produces a 32-bit word of output.
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.
To certain extent, LTE provides "somewhat" end to end security. Contrary to what @D.W said, (I am assuming what he meant by wired network is probably core network - i.e. after base stations), 4G/LTE would use Diameter protocol and hence IPSec. So the legacy Signalling System no. 7 (SS7) like core network protocols will be replaced in LTE and hence authentication along with hop-to-hop access control is in place at least as per the specification.