Magic never boosts magic
Any spell-casting roll can never receive additional dice, re-rolls, 8/9 again or rote actions because of the direct effects of another spell.
All direct magical attacks are vulgar
Spells which deal direct damage to opponents are automatically vulgar regardless of which Arcanum is used to cast them. Example spells from the book such as Psychic Assault which were listed as covert should no longer be regarded as valid examples.
A character can take both a magical and a physical action each turn. This is to enhance the action/adventure feel of the game. Chanting in High Speech can be done as the character’s physical action granting its bonus to spells cast that turn, rather than for the next turn.
Relinquishing a spell
It no longer requires a Willpower Dot to relinquish a spell, this can now be done simply by spending a Willpower Point. (This is largely because extended casting has been removed).
Extended Casting no longer exists
Please disregard the rules for this from pages 120-121 of the Mage rulebook. All mage spells must be cast as instant actions using the fast casting rules. The example spells from the rulebook which have an action type listed as Extended should be viewed as no longer valid examples however they can usually be performed as an equivalent level Ritual Magic effect.
Attribute Increases are always vulgar
Any increases to attributes are always a vulgar effect.
Rotes from splatbooks should be regarded with extreme skepticism
Not that the main rulebook is perfect but any of the example spells you see in a splatbook shouldn’t be viewed as explicitly permitted. For the most part, the errata on this page is only addressing the main rulebook anyway so splatbooks should be regarded as not yet errata-ed at best, completely non-canonical at worst.