Learn English – “got” in “You’ve got to be kidding me!”

1. Forget the "order of tenses". There is a natural sequence past → present → future. Perfect forms, however, do not designate past events but current states brought about by the past events. A present perfect designates a state which is current 'now', and the events which brought about the state may have happened at any time before that, before or after some other event designated with a simple past.

2. Would, as you rightly observe, is a past form used with present reference to signify that the action represented by the verb sequence it heads is 'counterfactual' (or irrealis, or impossible). Would like consequently designates its object as something now wished for which now, in the present, has not happened.

3. The phrase to have seen is not, strictly, a present perfect — it is, rather, a perfect infinitive, the marked infinitive of HAVE + the past participle of SEE. It has no tense, and therefore can be employed in a complement to a verb with any tense.

Accordingly, "The fans would like to have seen some improvement this year" may be paraphrased as

The fans wish that they had seen some improvement this year[, but they didn't see it].

The real meaning of the idiom "Nothing to shake a stick at" is that something is not very impressive. Here is a reference to its origins. Another, more understandable, version is "Nothing to write home about".

At first reading, I thought is was appropriate, after all 1GHz processor isn't much these days, but the exclamation mark indicates that he was impressed at the time of writing.

He has probably mixed up his idioms. The "not sure why" is just a remark about the absurdity of the idiom.