1. If one slaughters a Korban outside the Beis ha'Mikdash before the doors of the Heichal are opened, he is exempt.
2. There is a dispute about whether one is liable for slaughtering a Korban Pesach outside the Beis ha'Mikdash when it is not Pesach.
3. One is not liable for offering an animal less than eight days old as a Korban outside the Beis ha'Mikdash.
4. One who offers a Hekdesh animal with a blemish outside the Beis ha'Mikdash is exempt.
5. The Se'ir la'Azazel may not have a blemish.
A BIT MORE
1. The closed doors of the Heichal indicate that it is not yet time for Korbanos. Therefore, had it been sacrificed even in the Beis ha'Mikdash it would have been invalid.
2. Some say that one is liable. Others say that one is not liable. A third opinion says that if one slaughters with intent that it should be a Korban Pesach, he is exempt (since it would have been invalid in the Beis ha'Mikdash); without such intent he is liable (since it would have been considered a valid Korban Shelamim).
3. The Gemara similarly discusses when one is liable for offering Korbanos, for people who are Tamei, outside the Beis ha'Mikdash when those Korbanos are not supposed to be brought yet (for example, offering the bird offerings that a woman who gave birth is supposed to offer outside the Beis ha'Mikdash, before she is supposed to offer them).
4. This is because the verse says that one is liable only if the animal could be brought as a Korban. Rashi understands that this applies even if the Hekdesh animal does not have a blemish and is merely dedicated for regular usage, not for sacrificial purposes.
5. This is derived from a verse regarding not offering animals with blemishes.