This sort of awareness is what separates experts from amateurs, in my opinion. While it's important in every type of game, it seems to me that House Baratheon and Tyrell in particular can't afford to get tunnel vision and have to keep a close eye on all parts of the board at all times.
One thing I've noticed lately is that my Baratheon wins tend to hinge on sea battles, and I've actually had more success conquering Dorne than beating Lannister recently. One tactic that I have developed to facilitate Bara wins is to strike fast, and then slow down. By this, I mean that you often have to take one of your neighbors by surpise in order to take Narrow Sea or East Summer Sea, but once you do that, move more methodically. The important thing is to maintain your sea control, and to that end it can be vital to take out White Harbor or Storm's End to sink the ships there. But usually it is a mistake to devote troops and premium cards/orders to taking castles quickly. Instead, focus on taking out the remaining sea forces in Shivering Sea or Sea Of Dorne, and spread your troops out carefully to secure barrels and prime raiding/support positions. Since Bara cards are so lacking in swords, an all out assault often fails to land a killing blow anyway, so a slower strangling process seems to work better.
One other thing is that a couple of my recent wins have been secured by having Patchface attack Martell when they are on their last card and removing Doran. I've found the Prince of Dorne can be a major spoiler, especially if he takes away your star orders right when you have drawn everyone's attention and are suddenly facing a triple team.
When attempting to win over land, I think the same lesson about moving methodically applies. With Bara's position, they can access 6 castles directly from their core territories, which means that you don't actually have to conquer anyone completely to secure a pretty sure win. You really don't need to go any further than Harrenhall/the Reach, so focus on keeping them secure rather than plotting more ambitious campaign.
That's my current thoughts, anyway.