If one of the services was performed at the proper time, for the purpose of bringing a different type of korban: Pesachim 59b-60b; Zevachim 2a, 7b, 8b-9b, 11a-b, 11b
If one of the services was performed at the proper time, intending to perform a later service for a different type of korban: Pesachim 60a
If one of the services was performed with intent for the korban pesach and for another korban, simultaneously: Pesachim 62b
If one of the services was performed with intent for the korban pesach and another service was done for another korban, sequentially: Pesachim 62b; Zevachim 2b
If one of the services was performed with intent for the use of people who are not members of that offering: Zevachim 2a, 4a, 7b, 8b-9b
Issues of intent in bringing a korban pesach outside of the time of the korban pesach
If it is brought with intent for a korban pesach: Pesachim 60b; Zevachim 7b, 8b-9b, 11a-b, 11b; Menachot 47b
If it is brought with intent for another type of korban: Pesachim 60b; Zevachim 11a-b, 11b
If one slaughtered the korban pesach outside its proper timeframe, with improper intent, it becomes a korban shelamim: Zevachim 7b, 8b-9b; Menachot 47b
If it is brought with intent for maaser beheimah: Zevachim 9a
If it is brought with intent for a bechor: Zevachim 9a
If it is brought with intent for a korban todah: Zevachim 9a
If it is brought with intent for a temurah [substitute] for another low-level korban [kodashim kalim]: Zevachim 9a
If it is brought with intent for a korban shelamim: Yoma 63a, Pesachim 60b, 64a; Zevachim 11a-b