Their Mars 2 and 3 probes could not wait for the Martian dust to
settle, their computers being preprogrammed and all. So the orbiters
took mainly images of a rather bland Red Planet:

http://www.strykfoto.org/mars3.htm

Of their two landers, Mars 2 did become the first human object to
land on Mars, but in what Western experts call a crashed state.
The Soviets proudly proclaimed it placed the Soviet Coat of Arms
on Mars:

http://www.mentallandscape.com/V_Pennants.htm

Mars 3 did land and started to return an image, but stopped
transmitting after 90 seconds. The Soviets blamed the dust
storm, but others claimed technical problems in the comm
section between the lander and orbiter.

The Soviets did try to beat the USA with the first Mars orbiter,
but the probe never left its Earth parking orbit: The timer for
telling the rocket to kick the probe into interplanetary space
was accidentally set to go off in one YEAR, not one hour as
planned. So what would have been Mars 2 became Cosmos 419
instead, one of many satellites dedicated to science by the
Soviets without going into any detail at the time as to exactly
what kind of science it was doing.