At Fatima Our Lady urged the faithful
to pray for the Holy Father,
she never mentioned criticizing him.
Of course you can - you have free will.
The pope doesn't speak ex cathedra with every utterance. Does he deserve our respect? Absolutely.
Steve Skojec has a very good post discussing the issue. It's well reasoned and is written in a very respectful tone. Many people get upset with media reports and Vatican press releases, as well as the daily homilies or comments reportedly from the pope. The pope himself can come off as pretty critical of all of us - no matter where we stand on the Catholic spectrum - traditionalist to progressive. I think he is often misrepresented however, and his name taken in vain, as it were, by those who seek to promote an agenda or defend themselves.
My biggest objection to criticism is that it often involves scoffing and ridicule, treating the pope as we might a presidential candidate we disagree with, or some public figure we despise. Sometimes the critics themselves seem to have serious issues wherein the crackpot blogger title is more than appropriate. I have no time for Emmerich prophesies or Malachi Martin insights, or drunken rants on blogs, but a frank discussion, respectful and considerate is not a problem - if one feels the need to discuss publicly what the pope really said.
Skojec notes: "It has become an increasingly common problem in the Catholic world these days to find ourselves in the unenviable position of being afraid to say what we really think. This is both institutional — imposed as policy (whether written or unwritten) on those who work for Catholic organizations — and personal — through the various mechanisms of self-doubt. If we notice patterns, problems, and consistent deviations from the mien of previous pontificates, who are we to raise such questions? To borrow a phrase, 'Who are we to judge?'” - 1Peter5
I'm not sure it is our place to judge. Likewise, those who take sides on any issue jump down the throats of those who disagree with them - therefore sometimes it is best to be silent - unless you want to get into a fight just for ego satisfaction, or you're Irish.
We live in confusing times and we aren't privy to what goes on behind closed doors. We may not even have a need to know.
I've written before that people have to be careful what they read, especially by people who claim special spiritual insight, discernment of spirits, and sensitivity to the 'signs of the times'. As Fr. Angelo Mary Geiger writes:
[T]he autonomous personal conscience sometimes lays claim to a false discernment when it sets private revelation and presumed personal graces against the magisterium. The desire for union with God sometimes leads individuals to attach themselves to extraordinary manifestations of the “spirit,” but in such a way that weakens their attachment to the Church. Thus, Catholics continue to embrace New Age spirituality, or some dubious private revelation, or a personal insight even though they know that their conviction runs contrary to Church teaching or discipline.
The discernment of spirits is so important today because there are many voices competing for our attention, and it is all so easy to assume that that what we hear, or even what we think and say comes from God. - Fr. Geiger
I think sometimes we have to step back and pray more and ponder in our hearts the things which confuse us - placing all of our trust in God alone. As St. John of the Cross taught his novices: "Take Lot's wife as an example, because she was troubled at the destruction of the Sodomites and turned her head to watch what was happening, God punished her by converting her into a pillar of salt. You are thus to understand God's will: that even though you live among devils you should not turn the head of your thoughts to their affairs, but forget these things entirely and strive to keep your soul occupied purely and entirely in God, and not let the thought of this thing or that hinder you from doing so."
"Keep yourself in peace and thousands around you will be saved." - St, Seraphim of Sarov