The way I see it, there are two facets to this question.
The dog's behavior
I agree with others in that it sounds like the dog suffers from at least mild separation anxiety. From the standpoint of trainer and someone that has dealt with dogs with extreme separation anxiety, I can tell you that it is not easy (and all-to-often-impossible) to fix, even with a knowledgeable handler with good resources. Just like humans, dogs suffering from anxiety will exhibit a variety of behaviors when their "person" is absent due to an overwhelming fear that the person will not return. This can include wimpering, barking, pawing at doors, salivating, eliminating inappropriately, destructive behavior, begging for attention/comfort from others, pacing, and generally acting-a-fool.
It is possible that the manager brings the dog to work because the dog is emotionally incapable of being left alone at home (even in a crate/kennel), and that the alternative might be euthanasia of the animal in extreme cases.
It is also possible that the dog is just rude and poorly trained. There are a lot of dogs like that out there, so I am not ruling it out.
Finally, people (very) often inadvertently reinforce undesirable behaviors. For example, if the dog is pestering you for attention, and you dismissively give him a few pats so he goes away, you just rewarded him for doing what you didn't want him to do. Likewise with the trash. If the dog is stealing objects to try and entire you into playing, and you go chasing him around the office, he just won.
What you can do about it
Honestly, if I had been bringing my dog to work for years and some new guy came in and started complaining, I know where I'd tell them to go. Getting the manager to change is probably a non-starter, and if you go "up the chain," you are likely to make a lifelong enemy. Instead, focus on what you can do to control your frustration (you'll have much better luck managing your behavior than you will someone else's).
Let me preface this by saying that if you are going to interact with the dog, make sure the owner is onboard with whatever you are going to do. There are both active and passive approaches to managing the dog's behavior, and I've provided some suggestions for both. Despite populate belief, training a dog doesn't take hours of drilling every day. If you use the right incentives and start simple, you could help resolve the problem behaviors by taking 5 minutes out of a couple of your breaks each day.
If the dog is making noises that distract you
Bring headphones. I work as a software developer and know all too well how important it is to have quiet when tackling a challenging task. If it isn't a dog barking, it is someone on the phone three cubes away that feels the need to yell into the phone, or a heated debate about current presidential candidates right outside my desk, or an impromptu drive-by meeting at the end of the row. Get yourself a decent set of headphones (I prefer either over-the-ear or earbud style because they have passive noise-cancelling capabilities). When you need to focus, put on something you enjoy (but doesn't offer too much distraction) and go to your happy place.
Also see below for the suggestion on training the dog some basic commands, as you could always redirect the dog to a behavior that is more acceptable to you.
If the dog is badgering people for attention
This is relatively simple to resolve. First, forget the term "people." If the dog is badgering someone else, that isn't your issue. If the dog is badgering you, simply and utterly ignore it. Don't acknowledge it whatsoever. Don't say a word, don't shoo him away, don't make eye contact, nothing. If he sticks his head under your arm, let your arm go limp. If he puts his head on your lap, keep staring at your screen and typing. If he climbs in your lap, act like he doesn't exist. It may take a while the first few times, but dogs are smart. The dog is badgering people for attention for the pure reason that it works. Stop rewarding the dog for behavior that you don't find acceptable. Dogs are smart, and he will quickly realize that his behavior doesn't get him anywhere and will either try something more productive or move on to easier targets.
Another option is to reward the dog for behavior that you do approve of (this is highly effective when coupled with ignoring behavior that you don't approve of). If the manager allows, look into training a "settle" or "go to mat" command. You can gradually work up the time until the dog will lie quietly by your desk for half an hour or more to get a tiny piece of a treat.
There are a lot of benefits to helping train the animal, with the biggest being that, as the dog starts to look at you as someone capable of providing direction, the anxiety issues may decrease when the manager is away. Dogs place a lot of importance on authority figures. You become part of the solution instead of part of the problem.
The dog is stealing items out of the trash
If there is a dog in the office, why are dog-edible items being left in perfect dog-height baskets on the floor? Like children, dogs only have so much self control. Yes, training goes a long way, but even a well-behaved dog will take something if the temptation becomes too great. It is no different than a child getting into the cookie jar. They know they aren't supposed to, but it is just too tempting. They eventually break down and take one, and, liking the reward, will continue to do so. Remove the reward (either by placing edibles in a different can that is harder to breach or putting the cans out of reach), and the dog has no reason to dumpster dive.
This is a good place to teach "leave it" and "drop it" commands as well. Teach the dog to leave and drop items on command, and trash becomes a non-issue.