(Note: I know Janeway has had some good moments, and, yes, I'm ignoring those right now. This writeup is about why I don't like her, if you want her praises sung, do it yourself.)
Janeway is, in my opinion, the worst captain of any of the series. I've been told by many people that this is because I'm sexist, not because she's poorly written and regularly fails to do her job properly. Of course, I'm always willing to give arguments against Janeway while those people simply keep repeating that she's the best captain and that I'm a sexist jerk.
When Voyager reached the Alpha Quadrant Janeway should have been tried and found guilty of unethical conduct and re-assigned to a non-command position on a science vessel.
This short list is a slightly modified version of by one originally posted on startrek.voyager on news.startrek.com by ONEofBORG:
We're in trouble, but it will be all better if we give some really, really advanced technology to our worst enemy!
Janeway wallows in self-pity rather than doing her job.
Well, I never actually saw the episode but most people I've talked to seemed to think that Tom's punishment was way too harsh. Demotion to Ensign and 30 days in the brig (Paris is claustrophobic) for doing something that she does herself often, and for worse reasons.
Janeway orders Neelix to tell Naomi the truth. I'm all for truth, but I'm also for parental rights. Her mother, Ensign Samantha Wildman, left Neelix in charge of Naomi. Janeway cannot order how somebody raises his/her child. Captain != God.
Torres says not to use the medtech on her "if there's any chance that it was gotten through torture of innocent people." They think it may have been, but Janeway orders it used to save Torres anyway. After it's been used on Torres, Janeway has the Doctor decide whether the tech should be deleted or not. So it absolutely should be used on an adult who doesn't want it used on her but perhaps shouldn't be usable for anyone else in the future, regardless of whether they want it used on them or not? Violating Torres' rights is bad, but to then violate the rights of anyone in the future who needs the tech to live by doing the opposite is really stupid. That shows that it wasn't forced on Torres for moral reasons (life must be protected) but because she didn't want to lose her Chief of Engineering. I considered the possibility that she just had a change of heart, but it sure didn't look that way: she had the Doctor decide whether to delete the program or not and then in the scene in Torres' quarters it's obvious she still thinks she did the right thing. (In my opinion, Torres has the right to choose whether it should be used on her and future people should have a similar right. However, if they don't have that choice then the same forced decision must be the same [different for each situation perhaps, but by deleting the program it now can't be used again no matter what the situation.])
Also note that in Dark Frontier they find the arm of a medical drone which they have no problem using. No tech gotten immorally there, right?
Janeway refuses to submit to another Devore inspection.
I submitted to your inspections before because you outgunned me, but I don't see any of your warships nearby. I have no intention of cooperating.
If you're in their territory, you should follow their laws. If Janeway didn't want to submit to the inspections she should have been willing to spend the "several months" (horrors!) it would have taken to go around Devore territory, particularly if you consider that she was purposefully and unnecessarily violating their laws by bringing telepaths through.
Also, they bully Turop (the wormhole expert) to get information from him. He's simply an innocent scientist who is helping them. They should be grateful he's giving them any help at all.
Janeway goes on a vendetta putting Voyager at risk because she's pissed at Ransom. She tortures (and risks killing) Crewman Lessing into telling her about Ransom's tactics—knowledge in no way required. She then confines Chakotay to his quarters for stopping her and for telling her that torture is wrong.
She tells the aliens that if they'll stop attacking Voyager she'll deliver the Equinox to them. When Tuvok points out that will be certain death for the Equinox crew she threatens to confine him to quarters too.
At the end of part two she even admits that Chakotay would have had good reason to mutiny.
Also, when the inspector in Counterpoint points out that they've made a lot of enemies (unnecessarily violating alien space, breaking their laws, etc.) Janeway simply says "We're just trying to get home." And the Equinox crew is any different? The ends don't justify the means.
Janeway: Coffee. Black.
Neelix: "Uh, sorry, Captain. We lost two more replicators this morning"
[Janeway puts hand on Neelix's shoulder]
"Listen to me very carefully because I'm only going to say this once: Coffee. Black."
[Neelix gets her coffee and hands it to her.]
Neelix: "While I've got your attention, there are..."
Janeway: "Coffee first."
Now I know people will lose their temper occasionally, but Janeway starts snapping at Neelix right off, refuses to do anything (I.E., her duty as captain) until she gets her coffee and is still rude after he delivers it to her.