After brewing for a long time and becoming familiar with starters, yeast problems, ales vs lagers, Belgian strains, German strains, English and American strains etc, I can say that I have used and seen most everything when it comes to yeast. Slow starts to starters or full batches of beer will happen even with the freshest of tubes. A brewer does not have control over what happens to the yeast prior to it arriving in his or her refrigerator. How is a home brewer to get control over such random situations? Additionally, yeast can be an expensive component in brewing, with a cost exceding 6 dollars for a batch, where the rest of the ingredients can cost less than 20 dollars. Some tips I have garnered over the years:

1) Yeast starters are important. They increase the yeast population, and will assure yeast activity when pitching into a batch. When yeast is near (or even past) the expiration date, do the starter 5-7 days in advance as this will allow it to start properly. If it is not going by brew day after this amount of time, it may not be suitable for brewing. More wort can be added to the yeast to keep it active on the chance that it starts quickly (sometimes it will even when old). When the yeast is more fresh, do the starter at least 2 days before. The starter will allow the brewer to inexpensively determine if the yeast is good or bad. Fresh yeast should start overnight, but may take longer if mistreated, and there is no way to determine mistreatment other than trying to activate it. FWIW the first batch that i make off of a fresh tube/starter is usually a lower gravity brew such as pale ale or pils.

2) Yeast can be re-used. It is a simpler process than most realize. I have been using a technique for years without any problems whatsoever. In a way, a brewer can treat a whole batch as a starter. Simply plan a series of brew days about a week in advance, and roll the yeast from one batch to the next.  Do the first batch as usual and after about a week, brew again, and transfer the first batch into a secondary carboy, and dump some of the yeast leftover from the first batch into the second batch. With ales this technique can be used up to 8 times without issue. Lagers should be limited to 4 re-uses or so. As long as the funnel (assuming that carboys are being used) and primary fermenter (again, carboys) are sanitary, there is no issue. The yeast that is loose on the bottom and pours easily is the active yeast, and the this technique I have found, does not pour enough spent yeast into the next batch to matter at all.
This method particularly useful for making high gravity brews. Higher gravity brews tend to have slower starts and can take longer if not much longer to ferment, but a large amount of yeast that is already going (more than in a single starter) can get this high gravity brew going quickly, and cut down the fermentation time.
For example:
What me and my buddy do is plan out a series of beers to brew. Lagers are for this example, as that is what we are doing as of this writing. We started with a Dunkles, then re-use the yeast on the next batch, a Dopplebock, doing the transfer and pitch a week later. The Dopplebock, being of higher gravity, fermented cold for 2 weeks, then was transferred and the yeast pitched into a Pilsener. The Dopplebock is still active at this time, and still fermenting, so it was kept cold and left aside to continue fermenting. The Pils was then transferred and that yeast used in a second batch of Pils. This yeast will be used once more in this run, a Maibock.

3) It is important to match the starter/re-pitch temperature to that of the new beer. For example, when re-pitching lager yeast mentioned above, the older fermenting batch was raised to approximately 60F, matching out target temperature for the chilled wort of the next brew. Starters should be matched temp wise to what the temp of the wort will be as well.This helps with a quick start as the yeast will not get a shock when pitched.

4) Hot weather brewing: As long as a carboy is being utilized, when temperatures are a bit warm for effective ale fermentations, a wet towel and some ice packs work well to cool off the fermentor. This also is a good method just to get the temp down of the fermenting beer in any situation, but keeping a wet towel on the fermentor will help insulate the beer from brutal Summer heat.

5) Make sure the wort is properly aerated. Do some research and choose an aeration method. We have an attachment on the end of our siphon that aerates wort transferring from the brew kettle to the carboy. In addition, we use a stone with a pump that uses air to aerate the wort once transferred into the carboy. The air pump is electric and there is an air filter in the system as well. This air pump can also be used in conjunction with an oxygen tank if one so desires for greater efficiency.

6) Yeast nutrients. Not that it is necessary, but greater fermentation efficiency can be achieved by adding a yeast nutrient such as Servomyces (in very small quantity) to the boil. I have used it, but to tell the truth, have not noticed any significant differences, though more research will be done on this soon.

7) This many feel is optional, but transferring beer off of spent yeast will help reduce any off flavors that dying yeast cells may infuse into beer. Rule of thumb is to transfer to secondary within a week of when fermentation is complete, which does apply more when a beer is sitting at room temperatures and not cold like a lager. I like re-using yeast for the next batch, so my brews usually are transferred to secondary after 1 or 2 weeks depending on how quickly the fermentation is going. Do not be afraid to transfer to another vessel after a week if fermentation is still going so that the yeast can be used in another batch. If beer has beed idle for more than a handful of days, I do not like re-using the yeast but will be certain to transfer to secondary and let anything left suspended in the beer settle to the bottom. Yeast autolysis is the yeast cells dying and the cell walls rupturing, releasing flavors to the beer that are meaty, rubbery, and sour. This can be hidden somewhat in bigger beers, but is more critical more delicat flavored brews such as pilsner.

Something worth mentioning: I read that every English brewer removes yeast from the top of the fermenting beer, and there are systems in use to do this without even handling beer. The idea here is to remove yeast at high kraeusen, before it starts falling back into the primary. this helps slow the fermentation process down and prevents the beer from fermenting out too quickly. It also prevents any off flavors created by too many dead yeast cells. This may not be something someone that brews in a carboy can do, but a bucket? Fuel for thought.