I recommend reading this translation of an interview with Qaradawi in full.
It contains a clear statement and exposition of the nature of his belief system.
It is evident, from the transcript, that he is, indeed, a moderate, in relative terms. He rejects the racist’s favourite canard – that the Jews of the Koran are not the Jews of today – and in any case thinks of judaism as a belief system, not an ethnicity. He speaks passionately of the obligations owed by muslims to dhimmis – a term he prefers not to use because “people think that the word dhimma is derived from dhamm [i.e., derogation], whereas dhimma means a pact and guarantee“. He goes on to say:
“We do not believe in violence, and we have denounced it whenever and wherever [it occurs]. I denounced the events of 9/11 and the kidnapping of hostages. I published communiqués on this matter, and I issued fatwa s some 18 years ago forbidding the hijacking of airplanes and the kidnapping of hostages. These things are well-known, Allah be praised. We do not believe in violence, and we believe that violence has no religion or homeland. There is violence in all countries and all religions… “
He has an interesting take on the culpability of jews for Christ’s non-cruxifiction:
“A few years ago the Vatican published a document proclaiming the Jews innocent of spilling Jesus’ blood, but whoever reads history knows how the Jews incited the Roman governor to crucify Jesus. We believe that Jesus was not crucified, but the crime was committed. Our Lord raised him to that, but what really happened was that he was really, and we believe that the Jews, I mean, they commit this crime. What was the question? [sic]”
He opposes racism.
But all in all, I’ve heard worse.
Have a read of his poem:
“Oh My nation, the struggle has become obligatory, so put aside chattering and screaming.
Put aside dallying. He who dallies and rests is of no help.
Put aside all pretence, since massacres and wounds have said their word.
The Missionaries of Peace are lying,
for there is neither peace nor pardon.
Weeping over the ruins of our camp is no longer of avail, nor crying.
We should no longer speak with words; rather let the spears have their say…
* * *
Oh men, the matter is grave. The time for jesting has passed.
Call things by their real names, for it is men’s way to be frank.
The veil has fallen from the face, and their secret workings are revealed.
The Crusaders have returned once more, and they move about in the [Iraqi] lowlands.
They spread perversion in the land, as though it were ground free for all to graze in.
They are again spilling blood, without shame of exposure.
And the Shi’ites play well the role assigned to them.
The treacherous role, whose beginning and end are known to all.
They returned when in the East there is no Nur al-Din in power, or Salah [Al-Din]. 
We have forgotten the past, but they have now scratched the scabs.
They did not recoil from slaughtering old men … or small girls.
Their hate is not slaked by the blood they spill with such arrogance and impudence.
They gleefully abuse the victims’ corpses, and violate the honor of women, fearing no retribution or punishment.
There is no Mu’tasim  to succor those who cry for help.
Don’t you see how conspiracies against Islam are hatched openly in the light of day?
Don’t you see how the land of the prophets suffers from wounds?
Don’t you see how the Jews commit outrages, while we excel in crying out?
They violated our Palestine, and declared that they will not leave it.
They heed not the censure of U.N. resolutions, nor any proposal…
Were it not for the firmness of young men, unwilling to part with their religion,
Young men who offer up their blood – and he who offers up his blood is blameless
* * *
Apostasy has become blatant, having no fear of exposure.
In the marketplace of hypocrisy plain falsehood is being peddled
Moral depravity is sold there under the name of art and openness
Perversion prevails arrogantly and openly day and night…
* * *
Oh Islamic nation, rise up and act! For there is no time to be lost.
Heresy has gathered its forces. Why are we frightened and fighting oneanother?
Assemble, and equip yourself as you can with that which is at hand.
Oh thousand million [Muslims], where are you when the wounds call out?
Bring one million from the billion, the select of the select.
One from every thousand, and with them we shall make war on all fronts…
* * *
There is no escape from producing men, this is like the making of arms.
The making of heroes is a science that was made clear in out tradition.
Heroes can only be made in our mosques, in the garden of the Koran, and in the shade of the true Prophetic traditions.
In the company of the righteous, who walk in Allah’s abode.
Those who guide by example, rather than by eloquence…
Those who betray the call to prayer, betray as well the call to struggle.
Oh my Islamic nation, stand fast, for night will soon give way to morning…”