You should rather clean or smooth the source point data than generate a TIN or raster and try to clean later.
Note that LAS data handling has greatly improved in ArcGIS 10.2. If 10.2 (with 3D Analyst) is available to you, try the build-in functions:
There is a tool called Locate Outliers (part of 3D Analyst) which works perfectly for removing spikes and such. Judging from the screenshot you provided this will most probably clean your spikes.
As your spikes seem to align, you could also use the Profile tool and carefully cut outliers manually along a swath profile.
For a more sophisticated filtering, you can classify your Lidar Point Cloud data (3D Analyst -> Set LAS Class Codes Using Features) and build your TIN using a subset of points (e.g. only points classified as surface).
Using other tools than ArcGIS
You could use FUSION Lidar Toolkit (open source), SAGA GIS (open source), LasTools (some parts require commercial licensing; ArcGIS Toolbox provided) or GlobalMapper/Lidar (also commercial) to manipulate your Point Cloud data.
If you prefer filtering a raster dataset, you can apply a median filter to eliminate spikes, but I highly recommend to filter your source pont cloud instead. Especially if your points are unevenly distributed, a single outlying point in a less dense area can produce a more widespread error in a corresponding raster dataset.