The phrase 'slight impact on' is correct and can be used in written English.
For example, "The new policy had a slight impact on the company's bottom line."
What's more, my mother tells me alcohol has a slight impact on one's impulsive decision-making, so the addition of "drinking" to the risk factors could simply imply that drunk people have more casual sex.
The contract dispute has already had a slight impact on Walgreen earnings.
The best aspect is meeting new people and seeing how I can make a slight impact on their life.
The text warns that "not keeping up with telecom news could have a slight impact on your career".
But there are hints that the Fed's rush to reduce interest rates has already had a slight impact on inflation expectations.
Experts also note that state tax credits and penalties have only a slight impact on many uninsured people, who typically pay little in state taxes.
Katie Couric's newsmaking interviews with the Republican vice presidential candidate, Sarah Palin, last week had only a slight impact on the ratings for her CBS newscast.
"We expect only a slight impact on Genentech's industry-leading growth," Geoffrey Meacham of J. P. Morgan wrote in a note.
An economic slowdown or hard landing will have only a slight impact on high-quality munis like California or New York bonds.
"This has resulted in a slight impact on waiting times, but we continue to admit, treat and discharge more than nine out of 10 patients within four hours".
A research report made public by the traffic commission last month said that a reduction of 10,000 permits would have only a slight impact on traffic flow in Manhattan.
