Whose influence on government reflected the poor leadership of the czar and the corruption of the Russian court during World War I?

It is quite difficult to exactly define the real influence of Rasputin on the Czar family or Russia and to separate reality from the legend created around this weird figure.

For sure it became a kind of confident/healer of the Czar family possessing magical or mystical powers that allegedly allowed him to alleviate the sufferings of the hemophilic son of the Czar, Alexei.
His influence was particularly strong on the Czar's wife, Alexandra, convinced that Rasputin, in several occasions, saved (magically) her son's life.

Due to the support of the Czarina and indecisions and incapacity of the Czar, Rasputin became more and more involved into politics, trying to influence governmental decisions and even military ones.

It is difficult to define the real damages caused by Rasputin in a period where in Russia everybody was against everybody in trying to damage as much as possible each other.

The reality was that the Army was poorly led and equipped (the generals were responsible for the few victories but in case of defeat it was always the Czar fault!), the politicians were quarrelling continuously among them with no regard of the nation's sake and the nobles lived an anachronistic medieval life of excesses and debauchery.

My sensation is that, yes, Rasputin was a weirdo with a strong influence (sometimes bad) on the decisions of a ruling Czar (that actually ruled very little) but certainly he was used as a scapegoat for the disastrous global situation of Russia at the time!