I really can’t claim to have followed Hodgson’s managerial career before Liverpool, so my fears are founded only on what I’ve seen with his games in charge of us.
Going into the season, the four glaring weaknesses in the squad were back-up striker, central midfield, left-wing and left-back. The only position addressed was left-back through the flogging of Insua and I would have expected that of any Premiership manager. I'll reserve judgment on central midfield as we've lost Mascherano and I have no clue of how good Meireles is. So, to sum up, the negatives:
i) Extremely ‘meh’ transfer window even with the resources at hand. Note the failure to prioritise the signing of a striker and winger over a left-back. If resources were a problem, Kelly/Agger/Aurelio/Wilson could have covered left-back until January. The lack of a back-up striker will cost us dearly. The only way we can ride this out is if Torres stays fit till January. Hodgson will be extremely lucky if so.
ii) Display of favouritism in signing players. He’s already signed two of his former favourites in Konchesky and Poulsen. I understand most managers have their favourites (e.g. Mourinho buying Carvalho), but Konchesky and Poulsen are players of a mid-table standard and have no business being at Liverpool. Having said that, I agree that they may do a solid enough job. However, their combined fee (3.5 million + 4.5 million) could have easily gone towards a striker or a winger.
iii) The Wilson signing (for about 4 million) was also a head-scratcher in terms of management of resources. We had (and still have) four centre-backs ahead of him. If resources were so scarce, why was money wasted on a young centre-back who is unlikely to see playing time this season?
iv) Poor team selection against Man City, Trabzonspor and WBA.
v) Failure to make substitutions at the right time against Man City, Trabzonspor and WBA.
vi) Playing Lucas and N’gog over two clearly superior talents in Shelvey and Pacheco.
A lot of the points above (those regarding transfers and Lucas/N’gog’s abilities) are based, of course, on personal opinions. However, the same are shared by several members on this site and are those, which I believe, will prove to be true over the course of the season.
The rest of the points (regarding team selection) are through observation of limited game time. So Hodgson might indeed prove them to be false. His lack of experience at the top level in the PL doesn’t have me too excited though.