The Ripple Effect of Changing Canon
In the last year or so I've seen a growing trend of authors ignoring major canon events or facts to make telling the story the author wishes to tell easier. Obviously if you're writing a non-canon 'ship you will have to ignore some aspects of canon. Even if you're writing a canon 'ship, unless you're beginning after the end of the series you'll veer away from canon eventually.
Sometimes things can be simply ignored; if you're a Xander/Anya shipper you may choose to ignore 'Chosen' and simply say in your author's notes that Anya survived the battle, or she did die but for whatever reason she's back. Now for the latter I would prefer to see the author take the time to explain how she came back. Even if it's just a summary of events between 'Chosen' and the point that the story picks up, it's always better to explain it in the story than to just put it in the author's notes.
There are some cases where canon cannot be ignored or changed that easily, and certainly not in an author's note. It may be acceptable to ignore it, or explain it away in a note if the fic is a one-shot piece or a PwP. It's acceptable at those times because the place to explain it in the story isn't going to present itself. However, if you're writing a twenty or thirty part fic and can't work in a simple explanation somewhere it's either bad writing or simply laziness. The explanations don't have to be long, or complicated, but they should be there.
The two things that I see this happen most often with are Willow being a lesbian, including Tara's existence and role, and Angel's soul. In both cases there are simple ways to work around the 'problems' and ignoring them altogether changes many things in canon beyond simply 'Willow was never gay' and 'Angel's soul is permanent'.
Willow's not Gay/Tara didn't exist
I'm dealing with this as one subject because they usually go together. As a Willow/Spike and Willow/Giles 'shipper I understand the need for Willow to be straight for the story to work. However if you're writing a post-season five fic, you have to take into account the affect Tara had on Willow's life, beyond just her sexual preferences.
Until Tara became a part of Willow's life, magic was important to Willow but her power was limited. She did spells occasionally but it wasn't something she relied on. After becoming involved with Tara, and having another witch to work with Willow began using more magic and taking more chances.
The first dramatic increase in Willow's power, and the first sign that she would be more susceptible to dark magic came when Glory attacked Tara. That was the first time we saw Willow use her magic out of anger; she had tried when she found Oz with Veruca but couldn't do it. It was emphasized more than once during that time that Willow was the only one powerful enough to hurt Glory. Would Willow or anyone else have discovered she held that much power if Tara had not been hurt? That same power was used again in 'The Gift' for Willow to restore what Glory had taken from Tara.
In the beginning of season six, Willow was confident she had the power to raise Buffy from the dead. She didn't believe she had that power in season five when Joyce died. If she had, she would've been willing to help Dawn, rather than just point her in the right direction. If she had not attacked Glory the previous season, would she have believed herself capable of raising Buffy? Would Xander or Anya have believed it?
As season six progressed her power grew further out of control, until Dawn was injured because of her abuse of power. I realize the abuse of power was increased because of Amy, however would Willow have figured out how to change Amy back if she hadn't been upset over Tara's departure? Would Willow have ever gone to Rack had she not been distraught over Tara's leaving?
This is the part that bothers me the most when I see a post-season six or season seven fic that uses the 'Willow's not gay/Tara didn't exist' author's note. Too many times this note is at the beginning and Willow still killed Warren, still became 'super-witch', still tried to destroy the world, and still had the power to activate all the potentials. This is the part where it's most important to give an explanation for things. Why did Willow do these things if not because of anger and grief over Tara's death? Without an event that was that traumatizing to her, it is completely out of Willow's character to kill someone, or to try to end the world. Would Buffy have believed Willow had the power to over-ride thousands of years of magic?
If you're going to ignore that seemingly small fact of Willow's being gay then these are all things that need to be considered first. You can ignore her sexual orientation but then you should also make the necessary adjustments to the rest of canon to work with the new Willow.
There are very easy ways to deal with Tara and Willow being a lesbian without using an author's note, and without diminishing Tara's importance in Willow's life. The first way, and the one I use most often, is that Willow is really bisexual not gay.
Making a case for this isn't that difficult. Tara was the first instance of Willow showing a preference for women. She dated Oz, she had a crush on Xander, she admitted to having a crush on Giles in high school. You can make a convincing argument that Willow loves the person, not the gender fairly easily. Then you've not discounted either relationship, both of which were important to the character's development.
The other way to avoid the author's note is to set your fic before Tara, or early in the relationship. If your fic is set before season five, you can easily explain that Tara left or the relationship was more experimental on Willow's part and didn't work out.
Angel's Soul is permanent
Angel's soul is permanent is an even worse offender for changing canon events than Willow's sexual preferences. To ignore the clause in the curse changes all eight years of the BtVS/AtS universe.
If this clause never existed, why did Angel lose his soul in season two? Why did Buffy have to kill him? Why did he leave Sunnydale? Why did Wolfram and Hart believe he may fight on the wrong side of the apocalypse? Why was he afraid to start a relationship with Cordelia? Or Nina?
The problem is that no matter how you want to 'ship Angel the soul is a problem. He can't truly be happy because he'll lose his soul. Unless you're writing an Angelus fic or a dark fic this is going to pose a problem. It is, however, a problem that can be fixed with a little effort.
A pre-'Innocence' fic, can always have Jenny finding a way to fix the clause, as she's the only one that knows of it at that point. You would, of course, have to go AU from early on that way, but it can be done, and is still better than ignoring it all together.
The time between 'Innocence' and 'Becoming part 2' there isn't really much you can do because he's Angelus so that's just a bad place to pick up a Souled Angel fic. If your fic is post-'Becoming part 2', the spell has been redone, by Willow. It was never made clear whether Jenny found the exact spell used to curse Angelus or a generic soul-restoration spell and it had simply been modified by her ancestors to include the happiness clause. Without that knowledge you can always explain that the spell Willow performed didn't include a happiness clause. This is something that can be known immediately or something Willow discovers later, whatever works best with your story.
These are a few of the ways that changing one canon event or fact can affect many other things, as well as a few ways around having to say to simply ignore these facts. These are far from being the only ways to solve these issues, or all the possible ways canon is affected by changes in small things. I do hope, however that this at least gives you a place to start to find a way to work within canon to write your non-canon fics.