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A decompiler that lets you directly edit a SWF and its code. In many cases this is all you need, but it doesn't edit "in-place" so you can sometimes get unwanted side-effects after recompiling.
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These command line tools let you insert and extract objects from SWF files without affecting anything else. The awkward part is that you need the name or ID number of an object first, which can be found easiest by using a decompiler.
SWFCombine lets you replace objects. My usual approach to removing something (e.g. white blob censor) is to find its ID with a decompiler, and use SWFCombine to replace that ID with a blank SWF file.
SWFCombine with the --dummy parameter will decompress a compressed SWF file without editing it, making it possible to hex-edit the file.
(Example: KooooNsoft's mosaic code can be disabled by finding each instance of the mosaic code in a hex editor and changing the object it points to, i.e. "render", to anything else)
SWFExtract lets you extract specified objects. The object can then be edited with a decompiler or imported into Flash, then later reinserted with SWFCombine, thus editing that specific object with zero chance of affecting anything else in the file.
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It's an open and well documented format. If you read into it enough you can write scripts to automatically parse a SWF and edit things that match certain conditions.
As an example, for this game you could probably automatically remove the mosaic code by writing a script that parses a SWF file one object at a time, and if it finds an ActionScript block containing the string "render" then it skips copying it and moves onto the next object. Unlike the hex-editor method mentioned above, this would remove the code entirely and possibly provide a tiny performance boost as a result.