Is there any program that gets all Word documents 100% correct? I remember, even MS's own WordPad messes up documents made with Word. Might be better to start from scratch with a different format than doc/docx I think.
Well WordPad isn't Word, so, that is to be expected. WordPad is really just Notepad with rudimentary processing.
And yeah, I don't think any program can get 100% compatibility with Word documents if they are originate--or are heavily edited--within Word. I suspect there is intentional coding behind this, but ultimately, it is what it is, due in part to the massive adoption of Word and a need for genuine compatibility between users in the business world. For personal use, for things that are only in the home, I definitely recommend going elsewhere. But if you work with documents in any kind of business or otherwise professional sense, it is worth going with Word IMHO.
Compatibility is also why I stick with making PDFs from Word when sending any kind of document that is intended to be static and doesn't need digital signatures or form fill, or otherwise shouldn't be edited directly. If I send a resume or something out to someone, with a PDF I can guarantee they see exactly what I want them to see. It's really a crapshoot if they are using an old version of Word or a free office app.
For those on Windows who aren't excessively focused on "libre" applications, Windows 10 will very much help with this, because there will be versions of the Office Suite applications that are available/bundled free. They aren't as advanced as the paid suite, but they are more than capable for a lot of the ordinary usage scenarios.
Microsoft is beginning to realize that home users should be given advanced capabilities free, the majority of licensing always came from the enterprise environment. Heck, with Microsoft HUP, you can get Office for what, $10 or $20, if your business has a certain type of license with Microsoft. So in essence, some businesses are basically paying for the employees to grab Office Pro for chump change, and it's not a per-sale fee either, businesses pay the same amount for that license regardless if an employee even takes advantage of the home use deal.
I've been getting Office that way for the past two generations, and fully plan to get the next version, though hopefully I can get that for Mac, as I'll be plenty happy keeping Office 2013 on Windows, I don't suspect I'll need further functionality. But Office 2011 for Mac is way behind.