The phrase "a mistake to support" is correct and usable in written English.
It can be used when discussing the implications or consequences of endorsing or backing a particular idea, action, or decision that is deemed incorrect or unwise.
Example: "In hindsight, it was a mistake to support that initiative, as it led to unforeseen complications."
Alternatives: "an error to endorse" or "a misstep to back".
"The Americans are making a mistake to support any change that will lead to the control of extremists and the Muslim Brotherhood," General Saleh said.
"European countries do not agree with the White House Middle East policy and think it is a mistake to support Ariel Sharon's purely repressive policies," he said.
Nevertheless I think it is a mistake to support a profession-wide military boycott or a public counter-counterinsurgency loyalty oath.
Gregory asks if it's a mistake to support the stimulus.
It is a mistake to believe a feminist must support someone because of their anatomy and not their actions.
This page felt it was a mistake to invade Iraq without broad international support, and since then we have seen few indications that Mr. Bush's notion of establishing a stable democracy there is anything but a dream.
Thus, since there are no competing hypotheses, it is a mistake to think that mathematics receives confirmational support from empirical evidence in the way other scientific hypotheses do.
It would be a mistake to infer from these elections broad support for one of Republicans' key talking points.
Markus Kaim, director of the Berlin foundation Wissenschaft und Politik is also taking a critical stance: "We see now that it was a huge mistake to not support the Syrian opposition, that was fighting ISIS in Syria at the time," he told German radio station NDR.
Simply stated, it's a mistake to paint this community with a broad brush, and assuming that one issue can win widespread support is a mistake.
In her view, Mrs. Clinton is making a mistake by continuing to support the war in Iraq, to the extent that she is mollifying voters nervous about a female candidate.
