We can't trust the Alexiad, but that's a good thing. Leaving aside the deeper philosophical issues behind the question of what is "actual history", it's still worth noting that every source is biased and no source will ever allow us to know exactly what happened. Historians instead piece together an interpretation of the past through the use of all the available sources, in the process judging which piece of information is more likely to be reliable or accurate in their subjective opinion. No historian should ever say that we know exactly what happened, because we don't, all we have are our own interpretations and pet theories. The same goes for primary sources - they only provide one perspective into the past. Even someone as privileged as Anna Komnene will never know all the details of her father's life, and Peter Frankopan even argued recently that Anna had a poor grasp of the chronology. Her knowledge of military matters is also weak, perhaps because she got the gist of the narrative from her husband, but misunderstood them due to her inexperience. Her account of the campaigns against the Pechenegs is I think particularly confusing because of this. Memory after all is a very fallible thing, especially when she had to rely on others for events she never experienced herself.

You have already pointed out that the Alexiad has many issues, particularly about it being Komnenian propaganda. I'm inclined to agree, but I think we should instead embrace Anna's bias and use it as a tool to further our understanding of Byzantium. This is because bias actually adds to our knowledge. Propaganda is especially useful, as it shows us what an individual or an institution wanted to be seen as and what their priority was. It also tells us a great deal about the context it was written in, which can often be more illuminating than what the source is meant to be an account of. Anna for instance actively ignored the role of his brother in her history, which tells us a lot about her attitude towards John II Komnenus and her opinions on who should have succeeded Alexios I; Anna had of course been confined to a monastery after her plot against her brother. Like all sources, the Alexiad is also a literary production and facts were often deemed to be less important than literary topoi by the author. Again, a big problem for historians looking for political or military factoids, but at the same time it is also evidence for the literary culture and quality of education at the time - so inaccuracies from one perspective can be a wonderful thing for specialists in Byzantine intellectual history.

Even though we know that the Alexiad is problematic, we can also read between the lines and use other sources to get a vague idea of what Anna was concealing (deliberately or not so deliberately - plenty of people make mistakes or put emphasis on the wrong thing without being malicious!). One example would be her manipulation of the chronology. She placed Alexios' revolt against emperor Nicephoros before the Norman invasion, when from Norman sources it seems like the Normans had already invaded when Alexios staged his coup. It would appear therefore that Alexios was given the command of an army to fight the Normans, but rather than being a loyal general, he turned around and used it to overthrow the emperor. Not exactly the epitome of righteousness he was depicted as by his daughter! More mundane matters, such as Alexios being on campaign against his enemies with important nobles and his family members in tow, may also indicate that his reign was a great deal less secure that a surface reading of the Alexiad would suggest - in this example, by gathering all the important aristocrats around him, he could at least keep an eye on them rather than leaving them behind to potentially plot against him in Constantinople. Other sources also add to our understanding of Alexios for matters not covered by Anna. A Frankish source for instance attests to the recruitment of Frankish knights for Byzantium before the First Crusade, and Byzantine seals found in London may suggest that Alexios' recruiters were venturing even further afield in order to hire mercenaries.

So yes, the Alexiad is a very problematic source, but at the same time it is also a very useful one. Without its problems, our knowledge of Byzantium in this period would be much poorer. With it, we not only have a very good read, but also a unique insight into an important emperor from the perspective of a clearly very intelligent imperial princess. It may be an unreliable perspective, but that's pretty normal for primary sources and its inherent unreliability makes it useful. History is never very tidy and we need messy sources like the Alexiad to understand how confusing it can be. For further reading, check out the work of Peter Frankopan, particularly his very readable The First Crusade: The Call from the East (2012). For something a bit more academic, consider Alexios I Komenos: Papers (1996), which is a collection of papers from leading academics talking about the emperor's reign as a whole. There isn't any up-to-date book focusing exclusively on Alexios I right now, which is a shame - hopefully one will be written in the near future!

Almost all history is propaganda for someone or some viewpoint. Roman (and Byzantine) historiography had a long tradition of ameliorating Rome's defeats.

Livy has a well-deserved reputation for being a pro-Roman propagandist, who also lived after the event that occurred (and long after anyone who witnessed the Second Punic War died). When describing Rome's initial defeats to Hannibal, Polybius and Livy always divert blame from Rome, instead pinning it on the circumstances. The Roman army wasn't united, or the consuls were squabbling, or one (wise) consul wanted to wait but he wasn't in command that day because an upstart with questionable lineage was, or... The subtext is that a real Roman army commanded by a real Roman would never have been drawn into such terrible tactical circumstances in the first place, and wouldn't have suffered such humiliating losses.

It's your job as a historian to discover this subtext. You've found it in the Alexiad. But everything has a perspective. The Alexiad's is from the Komnenoi and the Eastern Roman Empire in general. If you read the sources from The Crusades through Arab Eyes and The Normans in the South, you'll find opposing (but equally biased) views. It doesn't mean that they're not "actual" history or untrustable. It means historiography matters to get an unbiased view of history.

Yeah as someone else pointed out sources aren't either accurate and thus history or inaccurate and thus useless.

ALL sources are useful for something. What you need to know is what questions you want answered. This can then inform your choice of sources. History isn't a collection of "facts about what happened" Its the historical circumstance and different contemporary/later perspectivse on said circumstances.

There is no such thing, in my view, as unhistorical sources. There are simply sources and their possible biases.