Indeed fruits of inferior quality or rotten were not acceptable. The Rambam writes (MT Bikkurim 2:3)
We do not bring [first fruits] from the dates in the mountains, nor
from the fruit from the valleys, not from oil-producing olives that
are not of the highest quality, but rather from dates from the valleys
and fruit from the mountains, for they are of the highest quality.
If a person brought first fruits of inferior quality, e.g., dates from the mountains, figs that were perforated and had oil applied to
them, dusty and smoked grapes, they are not consecrated.
and 2:20
When a person set aside his first fruits and they rotted away [...] he is obligated to
set aside others in place of them.
Note however that bikkurim were not offerings in the sense of being offered on the altar, instead they were to be brought to Jerusalem in a procession, presented to the priests and eaten there (details here).