Looking at their starting squad:
GK:
Reina
Jones
Itandje
Reina is superb, one of the best their is, and Jones is a more than adquete backup (on my Pool save, he played all the way to xmas due to Reina breaking his leg, and averaged a 6.99 in the league, and 7.12 overall). Itandje is pretty poor, and buying Enyeama may be wise as he's so cheap, but this isn't a vital area for improvement.
RB:
Johnson
Darby
I've found Johnson to be quite injury prone, and Darby really isn't good enough for a top prem side, and has low potential. Carragher can provide cover, but he's not great either. Diego Renan (around 4.5m) or Gregory Van Der Wiel (Around 9m) are good, young choices here
CB:
Carragher
Agger
Skrtl
Kygyriakos
Agger is a great Ball Playing CB, and a left footer too - he's a definite starter imo, and did very well for me. For the right CB, Skrtl and Carragher are both great and I had them rotating, with neither particularly standing out. Kygyriakos is a decent backup (and can't be sold for much as he's old). No real improvement needed, but Mexxes is usually available around the 8.5m mark and is a steal every time if you wanna shift one of Kygyriakos, Carra or Skrtl.
LB
Konchesky
Aurelio
A really weak area of the squad, with neither being first team worthy. Coentrao is available for about 8.5m and is a great buy who can double up as a LW if required. Dodo is a good young choice too, but I've not got experience with him so no idea what he costs.
CM/DM:
Poulsen
Lucas
Mierieles
Shlevey
All good defensively, but none really stand out going forward, so depending on how you play, a signing may be needed here. Marek Hamsik is a great buy for around the 15m mark who always seems to pop up with key goals. Defour(5m) and Witsel (3.5m) are both great and young too.
AMC:
Gerrard
Babel
Both good, but more suited to other roles. Babel is better on the wing, and Gerrard does better as a MC. He'll still do great here though so not a vital area for improvement, but Pastore (25m) and Hazard (15m) are both future stars if you want someone to replace Gerrard as he's only got a few seasons left in him. With Maxi and Joe Cole both being able to provide cover, however, this isn't a vital area for improvement.
AMR/L:
Cole
Kuyt
Maxi
It's interesting to note there are no natural left wingers in the liverpool sqaud, though Babel and Jovanovic can both do well here. Definite need for improvement needed. For the right, you should be okay for a season or two, but Alexis Sanchez turns out amazing, though at around 20m he's pricey for a first season buy. On the left Zezinho is great (not sure about price -- 6m ish I imagine), and improves a lot. Diego Buonotte is a good too, but not a natural LW so will need to be trained there.
ST:
Torres
N'gog
Jovanovic
Torres is brilliant, one of the best there is, but highly injury prone. Jovanovic did well for me as a poacher, but didn't have Torres' ability in the air, or to turn a game around single handedly. N'gog is, well... N'gog. If you want a partner for him, Dzeko (21m) or Lukaku (7m) are good choices as target type players. For a backup, Gignac (11m) or Neymar (17m) are both great, with Neymar becoming a world beater (train up his finishing though!).
Hope that helps!