There are a few ways to help the SSA move at its highest possible speed - although much of what it must do with the medical or financial review takes time, because experts must be retained to provide expert medical opinion with regard to your condition as represented by your medical providers; it must also review you financially if your claim is SSI and not SSDIB, which means looking into its resources to determine if there are any undisclosed resources or forms of income.
The first thing is to check your mail and respond quickly to any information requests. Answer the questions asked accurately, and in a detailed way that will reflect how "abnormally" you function with regard to the given tasks inquired of. Then, make sure to have your attorney review and adjust your information in a timely fashion, before she sends the finalized docs to the SSA. Whenever possibly, I encourage my clients to use a fax or scanner/email to get me docs expeditiously. THe more they rely on the US mail, the slower their case takes. Also, I have the power often to upload docs to the SSA so we need not even rely on the SSA mail room to properly sort mail, and the document is automatically electronically put into the client's SS folder. So, instead of spending money on stamps, consider getting a cheap 3-4 way fax (printer, scanner, fax). For $50, it will save you money and time.
When your attorney seeks extra evidence (opinion evidence) from your medical provider(s), she may (as we do) provide you with a copy of that request. We do that so that IF the doctor doesn't get back to us speedily, the client/patient can also get on him and nicely request he fill it out on the spot at the next appointment. Getting this extra evidence can help reduce the chance of a denial, and getting it done early helps prevent a denial that one then has to appeal. THe more evidence you get in of the varying criteria the law spells out that MUST be found in order to be awarded, (particularly that which the SSA won't be asking for or searching for) the higher the chance of getting a positive award. So don't sit around expecting evidence to grow on trees, talk to your lawyer about any possible 'to be developed' evidence - as that is often what produces a win.
Most importantly - treat, treat, treat for ALL you ailments, consistently and regularly. Make sure your doctor documents ALL your complaints, of that particular day AND that general time period - even those he doesn't treat your for. That is not an easy feat, many drs don't take the time to put into your record what you say... and judges can use that "omission" to find that the complaint did not exist, that you were "doing well" - which he then finds inconsistent with disabling pain or other symptoms. If you have problems suitable for a specialist, don't wait for your dr. to refer you - respectfully ***** ***** he refer you. Same with diagnostic tests - to see which medical conditions have worsened, not improved, etc.(MRI, CT scan, etc.)