Some times, like just after waking-up, men have an erection. But what if one just woke up and wants to say the Mode Ani, must he wait for it to pass or can he say it as is? Would it be disrespectful or make an averah to say it as is?
Gabe, I just saw the Ramban write* about the human body, and how no part of it should be considered disgusting or ugly. This part, according to him, is just the same as a hand or a foot or a nose. Hashem made it. The fact that one has an erection should make no difference to his saying Modeh Ani, as long as he is appropriately covered for tzniyut reasons.
*(I should clarify - I didn't actually see him write it, I saw an excerpt from what he wrote, in a sefer for Kallah teachers).
modeh ani is said without washing ones hands when one is actually tamei. as soon as one wakes up in the morning the appropriate thing to do is to sit up and acknowledge the creator for returning your soul to you. this is done regardless of the state one is in. (tehilas Hashem annotated edition page 586 discuses saying modeh ani in a very bikitzur manner)
This is a great link... http://www.chabad.org/library/article_cdo/aid/1466224/jewish/Modeh-Ani.htm
In regards to machshava zaras. There is a difference between a thought that was thinks of and that one thinks about. We don't have control over what we think of. Thoughts can come and go and are random through out the day. What we decide to focus on though is a choice. The response though is not to stop thinking about something but rather to redirect ones thoughts on something else all together. Once one is focuses on a different subject the previous machshava zara will be gone b/c by definition you are thinking of a different thing now.
Much hatzlacha in your avoda. As always more specifics about these topics can be learned about from a mashpia. Everyone needs a mashpia like it says in pirkei avos aseh lecha rav