In the Batman movies, Batman is called when a powerful yellow spotlight with the bat drawing is projected in Gotham City's clouds. The unique drawing then become very clearly visible in the clouds on the entire city. Is this actually possible or at least plausible?
YES, it is possible to project images onto clouds, and it has been for quite some time.
A Sky Projector from 1931:
From Fortean Times:
By the late 1920s, Harry Grindell Matthews was back in Britain with a series of new, bold inventions which actually worked. His piece de resistance was a device to project advertisements on clouds.
On Christmas Eve 1930 he stunned London by projecting the image of an angel onto clouds above Hampstead Heath. The apparition was so realistic that people miles away apparently fell to their knees in worship, believing the Second Coming was at hand!
He followed this with demonstrations in New York, where he projected the Stars and Stripes 10,000ft (3,000m) above the city.
A more recent example:
From The New York Times (2008)
Like the giant Batman sign projected into the night skies of Gotham City, the text "Beware of the God" suddenly appeared in the Singaporean sky mid-September.
The 30-minute projection, repeated over several nights, was the work of Deborah Kelly, part of the opening week of the Singapore Biennale 2008.
Photos from Sydney (projected from the roof of the Museum of Contemporary Art ) can be seen here:
The key word is definitely "clouds".
In theatres, we do what is similar to the bat signal all of the time, with something called "gobos". Of course, gobos are typically pointed at something solid, which makes them work.
Pointed a gobo at a cloud would work, altough not as well, as clouds are not solid.
Now, if the bat signal needed to be used on a clear night... I am guessing that wouldn't work as well (or at all), since it wouldn't have anything to reflect back on.
Of course, having any flood light, using a special color would still probably grab the attention of the Dark Knight.