The simplest answer to this question is 'a lot', but before we even get to that, some of the assumptions you make cannot be right.
If free will is gone, that implies that the mind works as a collective, which seems to be the intent of your question. If that is the case however, then telepathy must be global. Distance and line of sight can have no meaning, otherwise there must still be some sense of independence remaining to the individual that allows 'it' to function when isolated or alone.
I'm going to assume global telepathy for the rest of this answer as it's closest to the spirit of the OP.
From a psychological perspective, the egocentric nature of our minds would be shattered almost immediately. The fact that a single mind can now see a situation from 2 or more perspectives, sharing the emotional and physiological symptoms that help drive that perspective, means that the ability to differentiate between 'my' thoughts and 'our' thoughts hasn't had time to form before the experience begins. That effectively wipes out the sense of self as an organism, and instantly reasserts it as a collective.
That said, if the emotions and physiological sensations (burning, pain, cold, hunger, fear, etc.) are part of the telepathy, a single mind could be overwhelmed by the maelstrom of different sensations coming from other minds. This in turn could cause confusion. How do you know to take your finger from the flame when (if there's 5 of you in the collective) there's only a 20% chance it's your finger burning? How do you think through the constant distractions?
Sure, everyone would now be equally good at chess, engineering, poetry, etc. The human mind stores a lot more than that however. What about someone with poor body image or low self-esteem? That person's sense of body image and scenes of itself in the mirror are now transmitted throughout the collective, along with the sense of revulsion that these images engender. The opposite is also true of those with acute narcissism. How do we reconcile such personal thoughts into a collective?
Not to mention that one of the collective once stole from another member, who never found out about it before. Oops, how do we manage that little piece of information? Knowing everything another person knows is sometimes less than helpful; even dangerous.
This assumes normal mental health. How do we integrate schizophrenics? Their very sense of reality is distorted and even though it can be argued that the broader collective should be able to filter out the hallucinations and other distortions of their reality, what if they just get integrated into the prevailing world view (meaning that the entire collective is just a little unwell)?
Then, you have blind or deaf people. They're (all of a sudden) bombarded with a massive amount of sensory data that they don't know how to process and that probably doesn't make immediate sense to them. That confusion is then transmitted to the rest of the collective. Our pool is needing a dose of chlorine by now, but wait! There's more...
Children. Other adults with learning difficulties. They are now bombarded with images, only some of which are PG or lower rated. That time you watched Texas Chainsaw Massacre, that wedding night you had 20 years ago; the 6 year old that just joined the collective has unrestricted access to it. Again, one can argue that the wealth of information assaulting a child's mind would put all those experiences into context instantly, but it's assuming that the neurochemistry of a young mind can handle that kind of connection and that kind of instant learning and rationalisation experience.
I'm assuming that this 'network' is effectively a peer to peer experience, and that therefore every mind contains a slightly differently nuanced set of complete experiences and memories of the collective. As the collective expands, this means that whatever process the telepathy takes place with eventually gets saturated in terms of bandwidth. Just how much information can be bombarded into a mind new to the collective and how do you manage the order in which it appears to allow for things to be integrated in a normal manner?
We haven't even touched on the new alignment of interest within the collective, and whether or not it would be willing to sacrifice a person (node) within it for its own survival or advancement. Does that person realise that he or she is being sacrificed? Does that have an impact on the collective? How is food allocated during shortages and the like? Self interest is a very confusing issue in such a hive mind. It can cause all sorts of paradoxes and conflicting answers before it gets resolved.
Perhaps the biggest danger of all is homogeneity. If we're all the same, and we all have access to the same information, where is the need to learn something new? Where's the competition in life that makes us stronger? Where's our need to grow? A hive mind is just as likely to stagnate and be unable to adapt to new conditions quickly as it is provide any advancement to our way of thinking.
Personally, I'm against it and I think it would cause more issues than it would solve. But then, I'm a private person and keep a lot of things to myself (when I'm not answering questions here). All that said, the idea that we would understand each other in such a configuration I suspect is surface thinking and hasn't been explored down to the levels beyond the knowledge that we could gain on an academic front. Not only that, but I deeply suspect that the chorus of perspectives would make that knowledge unusable because of the poor signal to noise ratio.