[susan53]

it's not grammar so much as ambiguity of meaning. The problem is the sentence :

Over the last three seasons, Mike has been playing very well, but he narrowly missed the mark.


Because of the choice of verb form, it's unclear what you mean. Do these "3 seasons" include the current season or not? If they don't, so that everything is completely past, it should be :

Over the last three seasons, Mike played very well, but he narrowly missed the mark.

If on the other hand you mean the last two seasons plus the current season, it should be :

Over the last three seasons, Mike has been playing very well, but in the last two, he narrowly missed the mark.

or :
Over the last three seasons, Mike has been playing very well, but up to now, he has narrowly missed the mark.

I don't like the use of "Finally very much either. I'd suggest :

Over the last three seasons, Mike played very well, but he narrowly missed the mark. Then, in the first half of the current season, he played even better and quickly increased his goal tally to the required mark.

This presumes of course that we are now in the second half of the current season - so that the first half is past. If not, if we are still in the first half, it should be :

I]Over the last three seasons, Mike played very well, but he narrowly missed the mark. However, in the first half of the current season, he has played even better and has quickly increased his goal tally to the required mark.[/i]

In this case I'd change it to : However, this season, he has played even better and has quickly increased his goal tally to the required mark even though the season is not yet half way through

So it all depends on what you mean. Which season are we in - the third or the fourth? And which part of the season? the first half or the second? Verb forms express time - here you need to show whether you're referring to periods which are completely past(eg the previous 3 seasons) or past to present and ongoing (eg the two previous seasons and this season).