Moving from liquid phase to solid phase solves a number of problems in peptide synthesis, most related to purification. So long as your growing peptide is on the resin there’s no need for liquid/liquid extractions or flash chromatography, because at the end of every reaction your reagents are flushed down into the waste bottle.
Unfortunately, purity can still be an issue. I’ve never seen the surface of one of the solid phase resins under a high powered microscope, but given that the beads swell and shrink in different solvents I’ve always imagined them a little like half-shriveled raisins. Sites caught in the clefts are going to be sterically hindered, so you can expect coupling reactions there to proceed slower, even in the absence of secondary structure on the growing peptide itself. This is a big deal, because if anything less than 100% of these sites react each cycle you’re going to end up with peptides missing one or more residues at the end, and such compounds tend to be somewhere between difficult and impossible to separate from your final product. Fortunately, there’s a few things you can do.
If at first you don’t succeed… When you are expecting a difficult coupling running the coupling reaction two or three times can really boost the yield, and is generally more successful than simply increasing the reaction time. Switching to a more active coupling agent can also help, following the series:
OPfp esters/HOBt < DIC/HOBt < HBTU or PyBop or TBTU < HATU 
If you’re only making a short peptide (<10 AA), you can go a long way only using the chloranil test. Named for one of the two key ingredients, this test will stain the free amines on your resin, turning them dark red (primary) or dark blue (secondary). Proper staining (or its absence) will let you know if you can stop coupling, or if the resin needs an extra round. Tertiary amines and amides don’t appear to stain.
The procedure is rather simple:
1) Draw a sample of beads into a pipette and transfer them to a small, disposable test tube. Suspending the beads in DMF with nitrogen gas works well. This is a destructive test, so try to keep the number of beads to a minimum.
2) Add equal volumes of 2% chloranil and 2% acetaldehyde, both in DMF. The beads should change colour after about 15 seconds, and will reach their final dark colour after about ten minutes.
3) There is no step 3.
Once dissolved in DMF the chloranil will last approximately 8 hr at room temperature or about three weeks in the fridge. As it goes off the solution darkens and sensitivity is reduced. At full strength this mix will stain primary and secondary amines equally well, which makes it useful for both peptide synthesis involving proline residues and peptoid synthesis.
Capping the Resin
If you are making a longer peptide chain you can’t depend on perfect coupling at every step, especially as you move through the 10-20 AA region. So, the second best option is to cap any unreacted amines with an inert functional group, preventing further substitution at that site. This will of course reduce your overall yield, but will simplify purification at the end. This step can also be combined with repeated/improved couplings, as a means of identifying exactly where in the synthesis trouble is cropping up (when combined with mass spec, of course).
Add a freshly mixed 9:1 pyridine:acetic anhydride solution to the resin, with a final volume three times the height of the beads. Agitate for ten minutes, then drain the solvent. Repeat with a fresh 9:1 mix, then drain and wash the beads 3x DMF, 3x DCM, 3x DMF.
Note: This is a step with a number of different methods for accomplishing the same result. Other mixes:
4:1 DMF:acetic anhydride, followed five minutes later by 1.5eq diisopropylethylamine. Half-hour reaction time.
4eq Z(2CL)-OSu in 1:1 N-methylpyrrolidone:DCM, plus diisopropylethylamine. Five minute reaction time, and amenable to some automated synthesizers (the coupling agent is a solid, and relatively stable in NMP/DCM).
 From “Fmoc Solid Phase Peptide Synthesis” by Chan and White.