Predictive spending - The two things in this world that I have the least faith in are the existence of unicorns and Google's Traffic Estimator. What's the question that sends chills up every search marketer's spine? "How much should we allocate search?" Especially for new campaigns, this can be a nightmare because the data always fluctuates. With most other media, you can budget months in advance. With search, it's a hit or miss proposition. Budget too expensive and you wind up bidding on keywords that aren't ideal for your goals; budget too low and you could lose potential sales when your accounts cap out at noon every day. Even accounts that I've run for years with a mountain of seasonal data can still surprise me with search volume, and when you consider that most accounts aren't stagnant and are constantly adding keywords, ad groups, new creative, etc, it could be a hard task to pin down search spend for a marketing manager that must budget ahead for a fiscal year.
Solution: Use as many data sources you can to aim to figure out what the projected volume and click costs can be, but then set the expectation with your client or manager that maybe higher or lower. Search is a different animal - marketing managers need to know that we can't plan to the dime - there always needs to be some wiggle room.
Reach/Lack of inventory - All Search, including Paid Search is a pull medium. Obviously, there are great benefits to this sort of unobtrusive advertising, but the downside is that you can't get in front of people who do not know to search for your keywords.
Solution: Use other channels to promote your core terms - especially your proprietary terms which can have low competition. I know that when we run large display campaigns, our clients see search volume spike on their terms.
Standing apart in a crowd - I think we can agree that it's hard for three-line text ads to stand out on a Search Engine Results Page (SERP) filled with text. Compared with such dynamic creative like full-page ads, video ads, rich media expendables, etc, you have to depend on users to dig on the page to read your message.
Solution: Study your competitors' ads. If they all push price points, then talk about benefits. If they all mention "free", you can talk value. Keep monitoring the landscape and ensure you stay before the competition.