What do you do when a sysadmin is set in his ways, even though you can prove that the solution's he's using are potential hazards to security/integrity? Or in a case where your sysadmin is supposedly "senior" but makes rookie mistakes on a regular basis? (and then complains that noone else should be doing sysadmin work when you try and fix the issues!)
Without going into detail, this is definitely an issue to take to management if it can't be addressed effectively with the individual in question. I would try to engage the other person and give him the opportunity to explain his rationale', however, given the arrogance and ego often found in our industry, it wouldn't surprise me if he didn't appreciate such challenges to his "authoritay."
At that point, you should build a solid logical, financial, and pragmatic case to counter his broken practices and you should suggest a few alternatives (NB: complaining without suggesting solutions is called 'whining'.) At the very minimum, get a copy of "The Practice of System and Network Administration" and start looking for best practices. Put your concerns down in writing. Each organization has different attitudes toward 'argument from authority' (e.g. do textbook best-practices trump those from the local sysadmin or management or developers or Marketing?) If possible, leave a way for the senior admin to 'save face' to make it easier for them to change, without necessarily admitting they were wrong.)
I wouldn't worry so much about not 'being on the team'; it's one thing to be a destructive, disruptive or obstructionist element; it's quite another to make change a positive experience for everyone involved. That said, depending on how dysfunctional your organization is, your choices may be to change your job or change your job - either fix it or find someplace else less broken. That's probably an extreme case though; keep it depersonalized and positive, listen more than you speak, and above all keep a paper trail. :)
That's hard to determine.
In my experience, you need a champion (direct supervisor) to be aware of this situation, and understand the implication of not being "on the team".
Once you have a little backing, you can be a little more confident that your observations on security should be handed down to the sysadmin, and that conforming with policy should be more strictly adhered to.
Maybe instead of fixing the issues yourself, getting involved in "helping" fix the issues is the way to go.
I guess that depends on who you are asking... If the question is meant for a fellow sysadmin, then in my opinion, whatever the "rank" (senior, junior), sysadmins should help each other in fixing problems instead of making it a race, a competition or something like that. After all, you are working in the same workplace, you have common goal of keeping your company's infrastructure in working condition, what's the sense in fights, disagreements? As for the mistakes - everyone can have a bad day, just point the error and help fixing it.
This is a political issue, rather than a technical one. As has been mentioned several times already (because it's a good idea) going to management with your concerns is a perfectly valid way to address the problem. If that avenue is blocked for some reason, you're left with peer pressure. This becomes even more problematic if said admin is already seen as very senior and thus has a lot of clout. In that case you may not be able to do anything about it.
Document what you DO find. If it turns out their careless attitude gets them into hot water, having supporting documentation on hand can help reduce their clout with management and peers, which will in turn make it easier on you to convince others that you may know what you're talking about. That's a delicate line to walk, but if you're not willing to get another job because of this it can work out.
Inform your manager that you disagree with this and here's why and the risks associated with that. Keep hard copies of what was sent just in case it becomes necessary to defend that you brought up this concern and it was discarded. This also assumes the sysadmin isn't in your line to the executive where you are.
You could also ask the sysadmin why he does things a certain way as perhaps what you see as a rookie mistake is actually sensible for some other reasons that you don't know.
Those would be my suggestions along with noting that if you seem to meet a lot of resistance, you may just become apathetic to the whole thing.
If you work with others at the same level, band together with them against this individual. Not in a confrontational way, but in a supportive way. Such as, have someone propose the same fix as you if you have proposed it to him and he refused. If multiple people give the same idea, he might take it.
If you are alone, go to your immediate supervisor, or, if he is in that position, the next person above. Do your best to bring your concerns out, but not accuse him of being an idiot outright.
Maybe you need to find out why their doing something that way first, rather than just trying to "prove" them wrong. It may be that there is some service that requires a dropping of security.
It's always easy to suggest "improvements" if you're not resposible for a system - but I find one of the biggest factors to stability is unnecessary change, and the more changes people want the less stable a system become.
Then theres always the case of "I'll do it" - someone who isn't responsible for a system suggests an improvement that they will look after, then they leave and the sysadmin has to pick it up.
Maybe I'm your sysadmin?
The scenario you stated could be extrapolated to any other industry; accounting, agriculture, automotive (just to pick three from the same letter in the alphabet). If your documentation is consistent across a large portion of time (not just the stuff that he is mucking up) then it's more likely to be taken at face value.