Brandon,
Like you I was very interested in obtaining a job in law enforcement. I had applied in the area of 25-30 departments. It was brought up in one interview and the chief stated "I can see you are a very determined and focused individual." As long as you aren't DQ'd at a bunch of agencies I think it shows that you are serious about it and not just "trying" the cop thing. My .02

Anxiety

I don't know if multiple applications will be looked down on, but I doubt it.  It shows a seriousness on your part in becoming a LEO.

Well this is what I plan on doing.

I would like to apply with Portland PD and one other department that has a polygraph. If I fail the polygraph then I plan on applying to agencies that dont use one. I have nothing to lie about but I have many friends that have failed certain questions that even I know they were telling the truth. (drug usage)

Do you think agencies will look down upon to applying with a lot of departments. When I say alot I mean 20 -30 departments. I figure one of those would have to hire me.

First question:  yes, agencies do share applicant information.

Second question:  in my experience and that of persons I know personally, a failure with one agency generally will not garner an overwhelming amount of attention by the agency with which you are currently applying.

I did email a few agencies with the questions similar to your questions.  The answers I received from all is summed up as this:  yes, we do request application records from any other agencies with which you have made application.  We will administer our own polygraph and do not rely on polygraphs from other agencies.

I would assume that application records from other agencies are requested in order to confirm continuity in information provided in your application and background packets.  Polygraph testing is unable to make such a confirmation.

I was wondering lets say for example I applied to 20 police departments and I failed a few polygraphs and passed a few. Would Police departments look down upon this? If you fail one polygraph test and pass another departments test what would happen?

Does anyone have any examples for this?