As indicated below, I took a look at some of the papers linked in the document above. A number of them have legitimate interesting findings, but often not the findings the person linking them thinks they have.

There's a first block of papers linked with the assertion that adjuvants and antigen injection causes brain damage. Innate immune system stuff tends to go over my head compared to adaptive immune system stuff, unfortunately. But I noted that the injections given to rats to induce immune reactions (lipopolysaccharide to mimic bacterial infection, and a second mimic of viral DNA) were given in a way that mimicked an acute systemic infection of bacteria or virus. Although these acute challenges did affect behavior later in life in mice, I find it odd that simulating bacterial or viral infection would be used as an argument about vaccination. I have a hard time addressing the last paper on vaccine adjuvants increasing autoimmune reactions except to note that the experiment was in the context of 'hyperdoses' of tetanus vaccine antigen much much higher than you would ever give a person after a week of pretreatment with immune-sensitizing chemicals, and I'm not sure that you can use this in context.

There's another paper linked with the assertion that "The literature also includes randomized placebo test of a flu vaccine in children, followed by following their health for a sustained period. The vaccinees got 4 times as many respiratory illnesses as the recipients of placebo." This is an extremely incomplete examination of the paper. It is true that those who received the flu vaccine did report much higher rates of non-flu respiratory illnesses (think colds) than those that were unvaccinated. However, the authors note that the study design was based on self-reporting and that those who got the flu might be less likely to report less-severe diseases in a study designed to study the efficacy of the flu vaccine. Much more importantly, they note that the vast majority of excess colds were reported in a window about a month after the peak of the flu season the year that the study took place, and suggest that it is due to a phenomenon called 'viral interference' known from the days of the live polio vaccine. It turns out that when you get a viral infection and recover, the part of your body that just recovered from infection is very resistant to other unrelated viruses for 2 weeks to a month afterwards due to a temporary boost to the innate immune system that is unsustainable and goes away. It also occurs for a shorter period after live-virus vaccines like the flu-mist nasal spray, or the live polio vaccine. It is suggested that children that do not get the flu in a given year due to a dead-virus vaccine therefore do not have a month of protection from colds at the height of cold-and-flu season and show more colds as a result.

Lastly of what I had time to look at, there's a clutch of papers linked with the assertion that "Other studies, both human and animal, report that flu vaccines can damage the immune system." I have to say that this, too, is a major misinterpretation that sadly hides some interesting and potentially useful information from view. These papers do indeed find that children who are repeatedly vaccinated against the flu show lower levels of memory T-cells adapted against the influenza virus, and that their reactions are more strain-specific with few broad-spectrum cross-strain anti-influenza antibodies developing. This is not a 'damaged immune system' though - this is just the result of the way the adaptive immune system works. They were not measuring some abstract 'immune system function', they were measuring the reactivity of the immune system to a particular suite of antigens found specifically in flu viruses which have to be produced by an adaptive response, they aren't there from the get-go. When you get sick, your immune system gets a good look at a whole functioning virus for a long time and builds a very strong reaction against it, most of which regresses leaving memory cells behind. The immune reaction to a vaccine is much smaller than that against a live virus, and so leaves behind a smaller memory cell footprint - but since the vaccine DOES empirically reduce the risk of developing the flu, that reaction is obviously still enough to head off an infection or reduce its severity a lot of the time.

Of much more interest is the finding that dead-virus vaccines generate a few specific antibodies and reactive T cell clones that are very strain-specific while actual illness generates a wide variety which tend to be at least slightly cross-reactive across strains, and that early vaccination reduces the total amount of cross-reactive antibodies made later. This makes sense because again, as said above, a smaller reaction is generated and only the most immunogenic things will be reacted against. The fact that smaller amounts of crossreactivity are seen later makes sense in the light of a phenomenon known as 'original antigenic sin' - once you generate an immune reaction against something, your immune system is kind of corralled into being biased towards replicating that response later rather than generating a new better response because the memory cells which can multiply up to react outnumber the new lymphocytes that can start novel reactions from single cells. If your first few exposures to flu antigens result in strain-specific antibodies, they might provide less innate protection against a novel strain than a more broad-spectrum initial response that came from a live virus.

This is actually interesting. The dead vaccines might be locking people who get them repeatedly from a very early age into a somewhat more limited set of reactions against the virus. It might suggest that a live attanuated virus vaccination (like Flu mist) or one or two actual contractions of the disease at some point is preferable to build some crossreactive immunity early in childhood to decrease the severity of future contractions, if the risk of not always having a good specific seasonal vaccine on hand for some very novel pandemic strain is deemed high enough. The vaccine is always better to get for the strain in a given year, but might affect reaction to future novel strains. I hereby quote from the paper:

"Thus, annual vaccination against influenza is effective but may have potential drawbacks that have previously been underappreciated and that are also a matter of debate (7, 22, 37). By no means do we suggest halting annual vaccination of children, especially those at high risk for complications, such as CF patients. A number of studies have demonstrated that annual vaccination reduces the morbidity and mortality caused by seasonal influenza in children and is (cost-)effective (23, 34–36). However, long-term annual vaccination using inactivated vaccines may hamper the induction of cross-reactive CD8+ T cell responses by natural infections and thus may affect the induction of heterosubtypic immunity. This may render young children who have not previously been infected with an influenza virus more susceptible to infection with a pandemic influenza virus of a novel subtype. Therefore, we argue for the development and use of vaccines that could induce broadly protective immune responses in children. For example, it has been demonstrated that live attenuated influenza vaccines induce virus-specific CD8+ T cell responses (21, 23a). In addition, it has been demonstrated that live attenuated influenza vaccines are also effective against drift variants in children (1, 2, 19). The development of broadly protective vaccines has been on the research agenda for some time, and progress has been made (13, 17, 38, 43). Young children, whether they are at high risk for influenza-associated complications or not, may especially benefit the most from these vaccines."

I did not get a chance to look further.

EDIT: Just so everyone knows, immunology is NOT my specialty, by any stretch. I'm much more a very basic metabolism and eukaryotic cell biology guy, usually working in yeast. I've just kind of always found the adaptive immune system fascinating because of the way it uses evolution with a single organism to do what it does.